Business Smarts - Sample Module for Introduction to Statistics

Scenario I
A sample of 100 observations is found to have a mean of 428.2 and a standard deviation of 18.4.

1) What is the 90% 2-sided confidence interval for the population mean?

 a)  [431.2, 425.2].

 b)  [428.2, 431.2].

 c)  [425.2, 428.2].

 d)  [425.2, 431.2].

 e)  None of the above.

2) What is the interpretation of the confidence interval in 1)?

 a)  There is a 95% probability that the population mean falls within the
       interval range.

 b)  There is a 90% probability that the population mean falls within the
       interval range.

 c)  There is a 90% probability that the sample mean falls within the
       interval range.

 d)  There is a 90% probability that the population mean falls outside the
       interval range.

 e)  None of the above.

3) What is the 90% 1-sided upper bound confidence interval for the population mean?

 a)  (-∞, 430.6].

 b)  (-∞, 431.2].

 c)  (-∞, 428.2].

 d)  [430.6, ∞).

 e)  None of the above.

4) What is the interpretation of the confidence interval in 3)?

 a)  There is a 98% probability that the population mean falls within the
       interval range.

 b)  There is a 90% probability that the sample mean falls within the
       interval range.

 c)  There is a 90% probability that the population mean falls within the
       interval range.

 d)  There is a 95% probability that the population mean falls within the
       interval range.

 e)  None of the above.

5) What is the 90% 1-sided lower bound confidence interval for the population mean?

 a)  [431.2, ∞).

 b)  [430.6, ∞).

 c)  (-∞, 425.8].

 d)  [425.8, ∞).

 e)  None of the above.

6) What is the interpretation of the confidence interval in 5)?

 a)  There is a 98% probability that the population mean falls within the
       interval range.

 b)  There is a 90% probability that the sample mean falls within the
       interval range.

 c)  There is a 90% probability that the population mean falls within the
       interval range.

 d)  There is a 95% probability that the population mean falls within the
       interval range.

 e)  None of the above.

7) What is the 95% 2-sided confidence interval for the population mean?

 a)  [424.6, 431.8].

 b)  [424.6, 428.2].

 c)  (-∞, 431.8].

 d)  [424.6, ∞).

 e)  None of the above.

8) What is the interpretation of the confidence interval in 7)?

 a)  There is a 95% probability that the population mean falls outside the
       interval range.

 b)  There is a 5% probability that the population mean falls within the
       interval range.

 c)  There is a 95% probability that the sample mean falls within the
       interval range.

 d)  There is a 95% probability that the population mean falls within the
       interval range.

 e)  None of the above.

9) What is the 95% 1-sided upper bound confidence interval for the population mean?

 a)  (-∞, 430.6].

 b)  (-∞, 431.2].

 c)  [431.2, ∞).

 d)  (-∞, 425.2].

 e)  None of the above.

10) What is the interpretation of the confidence interval in 9)?

 a)  There is a 98% probability that the population mean falls within the
       interval range.

 b)  There is a 99% probability that the population mean falls within the
       interval range.

 c)  There is a 95% probability that the sample mean falls within the
       interval range.

 d)  There is a 95% probability that the population mean falls within the
       interval range.

 e)  None of the above.

11) What is the 95% 1-sided lower bound confidence interval for the population mean?

 a)  [431.2, ∞).

 b)  (-∞, 425.2].

 c)  [430.6, ∞).

 d)  [428.2, ∞).

 e)  None of the above.

12) What is the interpretation of the confidence interval in 11)?

 a)  There is a 98% probability that the population mean falls within the
       interval range.

 b)  There is a 90% probability that the sample mean falls within the
       interval range.

 c)  There is a 90% probability that the population mean falls within the
       interval range.

 d)  There is a 95% probability that the population mean falls within the
       interval range.

 e)  None of the above.

Scenario II
A sample of 225 observations is found to have a mean of 2,463.1 and a standard deviation of 784.9.

13) What is the 98% 2-sided confidence interval for the population mean?

 a)  [2,341.3, 2,584.9].

 b)  [2,584.9, 2,341.3].

 c)  [2,341.3, 2,570.6].

 d)  [2,463.1, 2,584.9].

 e)  None of the above.

14) What is the interpretation of the confidence interval in 13)?

 a)  There is a 95% probability that the population mean falls within the
       interval range.

 b)  There is a 98% probability that the population mean falls within the
       interval range.

 c)  There is a 98% probability that the sample mean falls within the
       interval range.

 d)  There is a 98% probability that the population mean falls outside the
       interval range.

 e)  None of the above.

15) What is the 98% 1-sided upper bound confidence interval for the population mean?

 a)  (-∞, 2,570.6].

 b)  (-∞, 2,584.9].

 c)  (-∞, 2,463.1].

 d)  [2,570.6, ∞).

 e)  None of the above.

16) What is the interpretation of the confidence interval in 15)?

 a)  There is a 99% probability that the population mean falls within the
       interval range.

 b)  There is a 95% probability that the population mean falls within the
       interval range.

 c)  There is a 98% probability that the population mean falls within the
       interval range.

 d)  There is a 98% probability that the sample mean falls within the
       interval range.

 e)  None of the above.

17) What is the 98% 1-sided lower bound confidence interval for the population mean?

 a)  (-∞, 2,355.6].

 b)  [2,355.6, ∞).

 c)  [2,463.1, ∞).

 d)  [2,341.3, ∞).

 e)  None of the above.

18) What is the interpretation of the confidence interval in 17)?

 a)  There is a 99% probability that the population mean falls within the
       interval range.

 b)  There is a 95% probability that the population mean falls within the
       interval range.

 c)  There is a 98% probability that the population mean falls within the
       interval range.

 d)  There is a 98% probability that the population variance falls within the
       interval range.

 e)  None of the above.

19) What is the 99% 2-sided confidence interval for the population mean?

 a)  [2,341.3, 2,584.9].

 b)  [2,328.4, 2,463.1].

 c)  [2,463.1, 2,597.8].

 d)  [2,328.4, 2,597.8].

 e)  None of the above.

20) What is the interpretation of the confidence interval in 19)?

 a)  There is a 99% probability that the population mean falls within the
       interval range.

 b)  There is a 99% probability that the sample mean falls within the
       interval range.

 c)  There is a 99% probability that the population mean falls outside the
       interval range.

 d)  There is a 98% probability that the population mean falls within the
       interval range.

 e)  None of the above.

Business Smarts!