Math 227 - Statistics » Spring 2023 » 17KC Testing a Claim About Two Proportions & Two Means Independent Samples

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Question #1
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. What population parameter is being tested?
A.   Linear Correlation Coefficient
B.   Proportion
C.   Standard Deviation or Variance
D.   Goodness-of-Fit or Independence or Homogeneity
E.   Mean
Question #2
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. How many populations are being tested?
A.   More than two
B.   One
C.   Two
Question #3
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. Calculate the sample proportion of men (round to the nearest ten-thousandth).
A.   0.0943
B.   0.0918
C.   0.0987
D.   0.0891
Question #4
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. What is the claim? (At this point, you should have already selected the formula that will be used to calculate the test statistic and written it in the test statistic box.)
A.   pW - pM ≥ 0
B.   pW - pM = 0
C.   pW - pM ≤ 0
D.   pW - pM ≠ 0
E.   pW - pM > 0
F.   pW - pM < 0
Question #5
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. The claim is the _________ hypothesis.
A.   alternative
B.   null
Question #6
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. What is the alternative hypothesis?
A.   pW - pM > 0
B.   pW - pM < 0
C.   pW - pM ≥ 0
D.   pW - pM ≤ 0
E.   pW - pM = 0
F.   pW - pM ≠ 0
Question #7
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. The critical region is best described as ____________.
A.   left-tailed
B.   right-tailed
C.   two-tailed
Question #8
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. What is the significance level (expressed as a decimal)?
A.   0.05
B.   0.01
C.   0.04
D.   0.02
Question #9
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. What is the critical value (rounded to the nearest hundredth)?
A.   -2.33
B.   -2.88
C.   -3.21
D.   -2.11
Question #10
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. What is the test statistic (rounded to the nearest hundredth)?
A.   -2.41, -2.40
B.   -2.44, -2.43
C.   -2.38, -2.37
D.   -2.54, -2.53
Question #11
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. What is the statistical conclusion?
A.   Fail to reject H0.
B.   Reject H0.
Question #12
Among 343 women surveyed, 15 worked the graveyard shift. Among 294 men surveyed, 27 worked the graveyard shift. The samples are independent and were gathered using simple random sampling. Use the critical value method and a 1% significance level to test the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift. What is the wordy conclusion?
A.   There is sufficient evidence to support the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift.
B.   There is not sufficient evidence to support the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift.
C.   There is sufficient evidence to warrant rejection of the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift.
D.   There is not sufficient evidence to warrant rejection of the claim that the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift.
Question #13
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. What population parameter is being tested?
A.   Goodness-of-Fit or Independence or Homogeneity
B.   Linear Correlation Coefficient
C.   Standard Deviation or Variance
D.   Mean
E.   Proportion
Question #14
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. How many populations are being tested?
A.   One
B.   Two
C.   More than two
Question #15
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. Calculate the sample mean of juice-fast dieters.
A.   -21
B.   -19
C.   -23
D.   -25
Question #16
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. What is the claim? (At this point, you should have already selected the formula that will be used to calculate the test statistic and written it in the test statistic box.)
A.   μJ - μP = 0
B.   μJ - μP ≥ 0
C.   μJ - μP ≤ 0
D.   μJ - μP ≠ 0
E.   μJ - μP > 0
F.   μJ - μP < 0
Question #17
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. The claim is the _________ hypothesis.
A.   null
B.   alternative
Question #18
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. What is the alternative hypothesis?
A.   μJ - μP ≥ 0
B.   μJ - μP > 0
C.   μJ - μP < 0
D.   μJ - μP ≤ 0
E.   μJ - μP = 0
F.   μJ - μP ≠ 0
Question #19
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. The critical region is best described as ____________.
A.   right-tailed
B.   two-tailed
C.   left-tailed
Question #20
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. What is the significance level (expressed as a decimal)?
A.   0.02
B.   0.01
C.   0.03
D.   0.04
Question #21
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. What is the largest critical value (rounded to the nearest thousandth)?
A.   2.234
B.   2.361
C.   2.136
D.   2.448
Question #22
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. What is the test statistic (rounded to the nearest thousandth)?
A.   1.369
B.   1.298
C.   1.552
D.   1.458
Question #23
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. What is the statistical conclusion?
A.   Reject H0.
B.   Fail to reject H0.
Question #24
Based on a simple random sample of 52 juice-fast dieters, juice-fast dieters mean net weight change after three months is -21 pounds with a standard deviation of 12.4 pounds. Based on a simple random sample of 61 paleo dieters, paleo dieters mean net weight change after three months is -25 pounds with a standard deviation of 16.7 pounds. Use the critical value method and a 2% significance level to test the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months. What is the wordy conclusion?
A.   There is not sufficient evidence to warrant rejection of the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months.
B.   There is sufficient evidence to support the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months.
C.   There is not sufficient evidence to support the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months.
D.   There is sufficient evidence to warrant rejection of the claim that juice-fast dieters and paleo dieters have the same mean net weight loss after three months.
Question #25
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What population parameter is being tested?
A.   Standard Deviation or Variance
B.   Linear Correlation Coefficient
C.   Proportion
D.   Goodness-of-Fit or Independence or Homogeneity
E.   Mean
Question #26
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What population parameter is being tested?
A.   Two
B.   More than two
C.   One
Question #27
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. Calculate the sample mean weight of professional athletes (round to the nearest ten-thousandth).
A.   184.7299
B.   183.2322
C.   185.5455
D.   185.1355
Question #28
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What is the claim? (At this point, you should have already selected the formula that will be used to calculate the test statistic and written it in the test statistic box.)
A.   μP - μN < 0
B.   μP - μN = 0
C.   μP - μN > 0
D.   μP - μN ≠ 0
E.   μP - μN ≥ 0
F.   μP - μN ≤ 0
Question #29
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. The claim is the _________ hypothesis.
A.   alternative
B.   null
Question #30
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What is the alternative hypothesis?
A.   μP - μN ≠ 0
B.   μP - μN < 0
C.   μP - μN > 0
D.   μP - μN ≤ 0
E.   μP - μN = 0
F.   μP - μN ≥ 0
Question #31
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What is the test statistic (rounded to the nearest thousandth)?
A.   1.843
B.   1.967
C.   1.371
D.   1.964
Question #32
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. The critical region is best described as ____________.
A.   two-tailed
B.   right-tailed
C.   left-tailed
Question #33
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What is the p-value (rounded to the nearest ten-thousandth)?
A.   0.0648
B.   0.0664
C.   0.0632
D.   0.0486
Question #34
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What is the significance level (expressed as a decimal)?
A.   0.03
B.   0.01
C.   0.04
D.   0.02
Question #35
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What is the statistical conclusion?
A.   Reject H0.
B.   Fail to reject H0.
Question #36
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What is the wordy conclusion?
A.   There is not sufficient evidence to warrant rejection of the claim that the mean weights of professional and non-professional athletes are the same.
B.   There is sufficient evidence to support the claim that the mean weights of professional and non-professional athletes are the same.
C.   There is not sufficient evidence to support the claim that the mean weights of professional and non-professional athletes are the same.
D.   There is sufficient evidence to warrant rejection of the claim
Question #37
  
A.   0.2872
B.   0.2937
C.   0.2332
D.   0.2778
Question #38
STATDISK has the ability to find test statistics, critical values, and p values when testing hypotheses about two independent population means. The next questions are designed to introduce you to these functions within STATDISK. For more information, please review the following tutorial. Always feel free to pause and/or restart the video. The claim being tested is μ1-μ2>0 with a 0.93% significance level. A first sample of size 96 with a sample mean of 270 and a sample standard deviation of 40 and a second sample of size 259 with a sample mean of 256 and a sample standard deviation of 32 are used to test the claim. What is the p-value? (Round to the nearest ten-thousandth.)
A.   0.0014
B.   0.0016
C.   0.0012
D.   0.0011
Question #39
The claim being tested is μ1-μ2<0 with a 12.49% significance level. A first sample (enter in column 1 of STATDISK) and the second sample (enter in column 2 of STATDISK) are below: First: 2, 9, 5, 6, 7, 8, 5, 2 Second: 3, 0, 5, 8, 7, 1, 8, 2, 5, 8, 7 What is the p-value? (Round to the nearest ten-thousandth.)
A.   0.6224
B.   0.6671
C.   0.6752
D.   0.6944

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