Math 227 - Statistics » Spring 2023 » 16KC Testing a Claim About a Mean & a Claim About a Standard Deviation or Variance

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Question #1
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). What population parameter is being tested?
A.   Mean
B.   Proportion
C.   Linear Correlation Coefficient
D.   Standard Deviation or Variance
E.   Goodness-of-Fit or Independence or Homogeneity
Question #2
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). How many populations are being tested?
A.   One
B.   More than two
C.   Two
Question #3
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). Calculate the sample mean (round to the nearest ten-thousandth).
A.   71.6553
B.   70.6458
C.   70.2481
D.   70.6464
Question #4
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). 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.   μ = 68.6
B.   μ ≤ 68.6
C.   μ ≠ 68.6
D.   μ > 68.6
E.   μ ≥ 68.6
F.   μ < 68.6
Question #5
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). The claim is the _________ hypothesis.
A.   null
B.   alternative
Question #6
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). What is the alternative hypothesis?
A.   μ ≥ 68.6
B.   μ ≤ 68.6
C.   μ > 68.6
D.   μ = 68.6
E.   μ ≠ 68.6
F.   μ < 68.6
Question #7
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). The critical region is best described as ____________.
A.   left-tailed
B.   two-tailed
C.   right-tailed
Question #8
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). What is the significance level (expressed as a decimal)?
A.   0.0
B.   0.05
C.   0.06
D.   0.04
Question #9
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). What is the critical value (rounded to the nearest thousandth)?
A.   1.799
B.   1.713
C.   1.796
D.   1.779
Question #10
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). What is the test statistic (rounded to the nearest thousandth)?
A.   3.447
B.   3.718
C.   3.113
D.   3.417
Question #11
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). What is the statistical conclusion?
A.   Fail to reject H0.
B.   Reject H0.
Question #12
John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. The results are listed below: 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5 John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men). What is the wordy conclusion?
A.   There is sufficient evidence to warrant rejection of the claim that women’s basketball players have heights with a mean greater than 68.6 inches.
B.   There is not sufficient evidence to warrant rejection of the claim that women’s basketball players have heights with a mean greater than 68.6 inches.
C.   There is sufficient evidence to support the claim that women’s basketball players have heights with a mean greater than 68.6 inches.
D.   There is not sufficient evidence to support the claim that women’s basketball players have heights with a mean greater than 68.6 inches.
Question #13
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. What population parameter is being tested?
A.   Linear Correlation Coefficient
B.   Proportion
C.   Goodness-of-Fit or Independence or Homogeneity
D.   Mean
E.   Standard Deviation or Variance
Question #14
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. How many populations are being tested?
A.   Two
B.   One
C.   More than two
Question #15
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. Calculate the sample mean (round to the nearest hundredth).
A.   98.4
B.   99.8
C.   98.8
D.   97.8
Question #16
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. 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.   μ ≠ 98.6
B.   μ > 98.6
C.   μ ≥ 98.6
D.   μ ≤ 98.6
E.   μ = 98.6
Question #17
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. The claim is the _________ hypothesis.
A.   null
B.   alternative
Question #18
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. What is the alternative hypothesis?
A.   μ ≠ 98.6
B.   μ < 98.6
C.   μ ≤ 98.6
D.   μ ≥ 98.6
E.   μ = 98.6
F.   μ > 98.6
Question #19
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. What is the test statistic (rounded to the nearest hundredth)?
A.   -2.68
B.   -2.88
C.   -2.13
D.   -2.19
Question #20
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. The critical region is best described as ____________.
A.   left-tailed
B.   right-tailed
C.   two-tailed
Question #21
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. What is the p-value (rounded to the nearest ten-thousandth)?
A.   0.0073, 0.0074
B.   0.0077, 0.0078
C.   0.0023, 0.0024
D.   0.0068, 0.0069
Question #22
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. What is the significance level (expressed as a decimal)?
A.   0.01
B.   0.04
C.   0.02
D.   0.03
Question #23
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. What is the statistical conclusion?
A.   Reject H0.
B.   Fail to reject H0.
Question #24
John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed. What is the wordy conclusion?
A.   There is not sufficient evidence to warrant rejection of the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed.
B.   There is sufficient evidence to support the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed.
C.   There is sufficient evidence to warrant rejection of the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed.
D.   There is not sufficient evidence to support the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed.
Question #25
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. What population parameter is being tested?
A.   Linear Correlation Coefficient
B.   Mean
C.   Goodness-of-Fit or Independence or Homogeneity
D.   Standard Deviation or Variance
E.   Proportion
Question #26
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: <pre>32 31 31 27 31 24 29 28 29 39 30 37 22 25</pre> Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. How many populations are being tested?
A.   Two
B.   One
C.   More than two
Question #27
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. Calculate the sample standard deviation (round to the nearest ten-thousandth).
A.   4.8018
B.   4.6011
C.   4.6016
D.   4.7191
Question #28
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. 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.   σ ≠ 5.0
B.   σ ≥ 5.0
C.   σ > 5.0
D.   σ < 5.0
E.   σ ≤ 5.0
F.   σ = 5.0
Question #29
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. The claim is the _________ hypothesis.
A.   alternative
B.   null
Question #30
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. What is the alternative hypothesis?
A.   σ = 5.0
B.   σ ≤ 5.0
C.   σ ≥ 5.0
D.   σ ≠ 5.0
E.   σ > 5.0
F.   σ < 5.0
Question #31
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. The critical region is best described as ____________.
A.   left-tailed
B.   right-tailed
C.   two-tailed
Question #32
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. What is the significance level (expressed as a decimal)?
A.   0.04
B.   0.03
C.   0.05
D.   0.06
Question #33
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. What is the smallest critical value (rounded to the nearest thousandth)?
A.   5.009
B.   5.007
C.   5.001
D.   5.008
Question #34
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. What is the test statistic (rounded to the nearest thousandth)?
A.   11.006, 11.005
B.   11.009, 11.008
C.   11.021, 11.020
D.   11.003, 11.002
Question #35
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. What is the statistical conclusion?
A.   Reject H0.
B.   Fail to reject H0.
Question #36
A highway engineer wishes to study highway speeds. Listed below is a simple random sample of speeds (mph) obtained at 4:48 PM on a weekday on the south 405 at Wilshire Blvd: 32 31 31 27 31 24 29 28 29 39 30 37 22 25 Use the critical value method and a 5% significance level to test the claim that the standard deviation of the speeds is equal to 5.0 mph. What is the wordy conclusion?
A.   There is not sufficient evidence to warrant rejection of the claim that the standard deviation of the speeds is equal to 5.0 mph.
B.   There is sufficient evidence to warrant rejection of the claim that the standard deviation of the speeds is equal to 5.0 mph.
C.   There is sufficient evidence to support the claim that the standard deviation of the speeds is equal to 5.0 mph.
D.   There is not sufficient evidence to support the claim that the standard deviation of the speeds is equal to 5.0 mph.
Question #37
STATDISK has the ability to find test statistics, critical values, and p values when testing hypotheses about the population mean. 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 μ<26 with a 4.59% significance level. Assume that the population standard deviation is known to be 5. A sample of size 96 with a sample mean of 27 amd a sample standard deviation of 4 is used to test the claim. What is the p-value? (Round to the nearest ten-thousandth.)
A.   0.975
B.   0.943
C.   0.819
D.   0.977
Question #38
The claim being tested is μ=-1 with a 1.84% significance level. Assume that the population standard deviation is known to be 0.94. The sample data below is the used to test the claim (enter into column 1 of STATDISK). 9, -7, -1, 2, -8, -7, 0, 7, -9, -2, -9 What is the test statistic? (Round to the nearest ten-thousandth.)
A.   -4.4906
B.   -4.3846
C.   -4.4712
D.   -4.2792
Question #39
  
A.   0.3228
B.   0.3208
C.   0.3341
D.   0.3109
Question #40
The claim being tested is μ>2 with a 11.59% significance level. The sample data below is the used to test the claim (enter into column 2 of STATDISK). 2, 5, 4, 5, 3, 1 What is the p-value? (Round to the nearest ten-thousandth.)
A.   0.049
B.   0.055
C.   0.051
D.   0.053
Question #41
STATDISK has the ability to find test statistics, critical values, and p values when testing hypotheses about the population standard deviation and variance. 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 σ<5.23 with a 6.67% significance level. A sample of size 163 with a sample mean of 62 and a sample standard deviation of 4.98 is used to test the claim. What is the p-value? (Round to the nearest ten-thousandth.)
A.   0.2032
B.   0.2067
C.   0.2088
D.   0.2049
Question #42
The claim being tested is σ2=95 with a 2.85% significance level. The sample data below is the used to test the claim (enter into column 3 of STATDISK). 7, 5, 12, 12, 12, 10, 3, 9 What is the test statistic? (Round to the nearest ten-thousandth.)
A.   0.8718
B.   0.8789
C.   0.8656
D.   0.8813

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