Math 227 - Statistics » Spring 2023 » 14KC Estimating a Population Mean & a Population Standard Deviation or Variance

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Question #1
A marketing firm wishes to estimate the mean age of college students. Assume that prior studies indicate that the standard deviation of college students ages is 2.04. How many students must the marketing firm randomly survey if they want to be 92% confident that the sample mean age of college students is within 0.33 years of the true population mean?
A.   118
B.   111
C.   108
D.   119
Question #2
The mean age of a sample of 40 college students is 23.95 with a standard deviation of 2.55. Construct a 98% confidence interval estimate of the mean age of all college students. What is the lower bound of the confidence interval? (Round to the nearest thousandth.)
A.   21.874
B.   22.729
C.   22.972
D.   23.298
Question #3
The mean age of a sample of 40 college students is 23.95 with a standard deviation of 2.55. Construct a 95% confidence interval estimate of the standard deviation of the age of all college students. What is the upper bound of the confidence interval? (Round to the nearest thousandth.)
A.   3.092, 3.144
B.   3.113, 3.168
C.   3.319, 3.369
D.   3.222, 3.274
Question #4
A marketing firm wishes to estimate the standard deviation of the ages of college students. How many students must the marketing firm randomly survey if they want to be 99% confident that the sample standard deviation of the ages of college students is within 5% of the true population standard deviation of ages of college students?
A.   1,663
B.   1,635
C.   1,148
D.   1,336
Question #5
STATDISK has the ability to calculate the cumulative area to the right under the student t distribution when supplied a t value. This function is equivalent to using Table 3 to find a range of possible areas corresponding to a t value between two t values or more extreme than an "edge" t value. Remember, Table 3 does not provide a robust method for finding the area under the student t distribution when supplied any t value. The next questions are designed to introduce you to these functions within STATDISK. The student t distribution function is located under the "analysis," "probability distributions," and "student t distribution" sub menu. What is the cumulative area to the right under the student t distribution with 156 degrees of freedom to the t value of 1.7896? (Round to the nearest ten-thousandth.)
A.   0.0377
B.   0.0239
C.   0.0333
D.   0.0371
Question #6
What is the cumulative area from the left under the student t distribution with 86 degrees of freedom to the t value of 2.2222? (Round to the nearest ten-thousandth.)
A.   0.9856
B.   0.9915
C.   0.8989
D.   0.9182
Question #7
STATDISK also has the ability to calculate the critical t value when supplied the cumulative area to the right under the student t distribution. This function is equivalent to using Table 3; however, the STATDISK function has the ability to supply additional critical t values not present on the table. Remember, Table 3 does not provide a robust method for finding critical t values for any area under the student t distribution. The next questions are designed to introduce you to these functions within STATDISK. The student t distribution function is located under the "analysis," "probability distributions," and "student t distribution" sub menu. What is the t value corresponding to the cumulative area from the left under the student t distribution of 0.1285 with 184 degrees of freedom? (Round to the nearest ten-thousandth.)
A.   -1.133
B.   -1.287
C.   -1.317
D.   -1.137
Question #8
What is the t value corresponding to the cumulative area to the right under the student t distribution of 0.7102 with 356 degrees of freedom? (Round to the nearest ten-thousandth.)
A.   -0.4595
B.   -0.5443
C.   -0.5545
D.   -0.5153
Question #9
STATDISK has the ability to construct a confidence interval estimate for the 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. A sample of 135 items resulted in sample mean of 14.09 and a sample standard deviations of 9.11. Construct a 95.21% confidence interval estimate for the population mean. Enter the upper bound of the confidence interval. (Round to the nearest thousandth.)
A.   16.515
B.   15.662
C.   15.115
D.   15.655
Question #10
Enter the following sample data into column 1 of STATDISK: 19, 16, 17, 8, 13, 2, 19, 8, 15 Construct a 87.89% confidence interval estimate for the population mean. Enter the lower bound of the confidence interval. (Round to the nearest hundredth.)
A.   9.19
B.   9.33
C.   9.63
D.   9.28
Question #11
STATDISK has the ability to find the sample size required to estimate a population mean. The next question is designed to introduce you to this functions within STATDISK. The sample size determination function is located under the "analysis," "sample size determination," and "estimate mean" sub menu. Determine the sample size necessary to estimate the population mean with a 96.07% confidence level and a 3.1 margin of error. Assume that the population standard deviation is known to be 9.74.
A.   44
B.   42
C.   46
D.   38
Question #12
STATDISK has the ability to calculate the cumulative area to the right under the chi-square distribution when supplied a chi-square value. This function is equivalent to using Table 4 to find a range of possible areas corresponding to a chi-square value between two chi-square values or more extreme than an "edge" chi-square value. Remember, Table 4 does not provide a robust method for finding the area under the chi-square distribution when supplied any chi-square value. The next questions are designed to introduce you to these functions within STATDISK. The chi-square distribution function is located under the "analysis," "probability distributions," and "chi-square distribution" sub menu. What is the cumulative area to the right under the chi-square distribution with 99 degrees of freedom to the chi-square value of 100.1878? (Round to the nearest ten-thousandth.)
A.   0.4774
B.   0.3447
C.   0.4177
D.   0.4477
Question #13
What is the cumulative area from the left under the chi-square distribution with 239 degrees of freedom to the chi-square value of 213.8059? (Round to the nearest ten-thousandth.)
A.   0.1327
B.   0.2222
C.   0.1221
D.   0.1431
Question #14
STATDISK also has the ability to calculate the chi-square value when supplied the cumulative area to the right under the chi-square distribution. This function is equivalent to using Table 4; however, the STATDISK function has the ability to supply additional chi-square values not present on the table. Remember, Table 4 does not provide a robust method for finding chi-square values for any area under the chi-square distribution. The next questions are designed to introduce you to these functions within STATDISK. The chi-square distribution function is located under the "analysis," "probability distributions," and "chi-square distribution" sub menu. What is the chi-square value corresponding to the cumulative area from the left under the chi-square distribution of 0.4098 with 111 degrees of freedom? (Round to the nearest ten-thousandth.)
A.   106.8829
B.   107.1248
C.   106.9826
D.   106.9966
Question #15
What is the chi-square value corresponding to the cumulative area to the right under the chi-square distribution of 0.0483 with 37 degrees of freedom? (Round to the nearest ten-thousandth.)
A.   52.5734
B.   51.4799
C.   52.3729
D.   53.1721
Question #16
STATDISK has the ability to construct a confidence interval estimate for the standard deviation or variance. The next questions are designed to introduce you to these functions within STATDISK. The confidence interval function for standard deviation or variance function is located under the "analysis," "confidence intervals," and "standard deviation one sample" sub menu. A sample of 68 items resulted in sample mean of 1.2 and a sample standard deviations of 6.4. Construct a 97.4% confidence interval estimate for the population standard deviation. Enter the upper bound of the confidence interval. (Round to the nearest thousandth.)
A.   7.614
B.   7.906
C.   7.966
D.   7.819
Question #17
Enter the following sample data into column 2 of STATDISK: 22, 91, 55, 70, 83, 26, 60, 19, 21, 21, 65 Construct a 88.11% confidence interval estimate for the population variance. Enter the lower bound of the confidence interval. (Round to the nearest hundredth.)
A.   421.55
B.   422.55
C.   422.51
D.   423.21
Question #18
STATDISK has the ability to find the sample size required to estimate a population standard deviation. The next question is designed to introduce you to this functions within STATDISK. The sample size determination function is located under the "analysis," "sample size determination," and "estimate standard deviation" sub menu. Determine the sample size necessary to estimate the population standard deviation with a 93.18% confidence level within a 7% margin of error.
A.   338
B.   339
C.   388
D.   318

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