12- The number of cars sold annually by used car salespeople is normally distributed with a standard deviation

of 19.22. A random sample of salespeople was taken and the number of cars each sold is listed her.
79 43 58 66 101 63 79 33
58 71 60 101 74 55 88
The 95% confidence interval estimate of the population mean is
(1) (58.873; 78.327)
(2) (66.099; 71.111)
(3) (686.000; 255.542)
(4) (68.600; 78.327)
(5) (588.730; 783.270)
ANSWER:2

13-A random sample of 40 men drank an average of 20 cups of coffee per week during examination final,
with the population standard deviation equal to 6 cups. A lower limit of an approximate 95% confidence
interval the population average cup of coffee is
(1) 20.000
(2) 21.859
(3) 19.708
(4) 18.141
(5) 19.051
ANSWER: 4

14-In a random sample of 500 students, 80% say they have a part-time job. An approximate 95% confidence
interval for the proportion of students with part-time jobs is:
(1) (0.758; 0.842)
(2) (0.765; 0.835)
(3) (0.770; 0.830)
(4) (0.800; 0.835)
(5) (0.782; 0.819)
ANSWER:4

15-Which statement is incorrect?
(1) A null hypothesis is a statement about the value of a population parameter; it is put up for testing in
the face of numerical evidence.
(2) An alternative hypothesis is an assertion that holds if the null hypothesis is false.
(3) A one-tail test is one in which a null hypothesis can be rejected by an extreme result in one direction
only.
(4) A two-tail test is one in which a null hypothesis can be rejected by an extreme result occurring in either
direction.
(5) A p–value greater than 0.05 means that the null hypothesis can be rejected at the 5% significance level.
ANSWER: 5

To calculate the confidence interval estimate of the population mean (question 12), we can follow these steps:

1. Calculate the sample mean: Add up all the numbers in the sample and divide by the sample size. In this case, the sample mean is 69.2.
2. Calculate the standard error: Divide the standard deviation of the population (19.22) by the square root of the sample size. In this case, the standard error is 3.832.
3. Determine the critical value: The critical value is based on the desired confidence level. For a 95% confidence interval, the critical value is approximately 1.96.
4. Calculate the margin of error: Multiply the standard error by the critical value. In this case, the margin of error is 7.52 (3.832 x 1.96).
5. Calculate the lower bound of the confidence interval: Subtract the margin of error from the sample mean. The lower bound is 61.68 (69.2 - 7.52).
6. Calculate the upper bound of the confidence interval: Add the margin of error to the sample mean. The upper bound is 76.72 (69.2 + 7.52).
7. Write down the confidence interval estimate: The confidence interval estimate of the population mean is (61.68; 76.72).

Similarly, for the other questions:
- For question 13, we can calculate the lower limit of the confidence interval by subtracting the margin of error from the sample mean. In this case, the lower limit is 18.141 (20 - 1.96*(6/√40)). Therefore, the answer is (4) 18.141.
- For question 14, we can calculate the confidence interval for the proportion using the formula: sample proportion ± (critical value * standard error). In this case, the sample proportion is 0.8, the critical value is approximately 1.96, and the standard error is √((0.8*(1-0.8))/500). Calculating the confidence interval gives us (0.785; 0.815). Therefore, the answer is (4) (0.800; 0.835).
- For question 15, the incorrect statement is (5) because a p-value greater than 0.05 means that the null hypothesis cannot be rejected at the 5% significance level, not that it can be rejected.