stats question

1) Lunch breaks are often considered too short, and employees frequently develop a habit of “stretching” them. The manager at Giant Mart randomly identified 22 employees and observed the length of their lunch breaks (in minutes) for one randomly selected day during the week. 31 22 39 35 26 34 22 28 27 20 27 35 30 27 26 32 25 24 29 32 27 42 (a) Show evidence that the normality assumptions are satisfied. Analyze the Normal Q-Q plot given below and determine whether or not the data has an approximately normal distribution. (Choose one)

a) The data appears to follow a straight line, indicating a non-normal distribution. b) The data appears to follow a straight line, indicating an approximately normal distribution. c) The data appears to not follow a straight line, indicating a non-normal distribution. d) The data appears to not follow a straight line, indicating an approximately normal distribution.

(b) Find the 95% confidence interval for “mean length of lunch breaks” at Giant Mart. (Give your answers correct to two decimal places.) __26.63_ to _31.55__ minutes

2) Determine the p-value for the following hypothesis tests involving Student’s t-distribution with 10 degrees of freedom. (Give your answers correct to three decimal places.)

(a) H0: μ = 15.1, Ha: μ < 15.1, t = -1 ______0.170____

(b) H0: μ = 15.1, Ha: μ > 15.1, t = 1.0 _______.170___

(c) H0: μ = 15.1, Ha: μ ≠ 15.1, t = 1.0 _______0.341___

(d) H0: μ = 15.1, Ha: μ ≠ 15.1, t = -1 _____0.341__

3) The recommended number of hours of sleep per night is 8 hours, but everybody “knows” that the average college student sleeps less than 7 hours. The number of hours slept last night by 10 randomly selected college students is listed below. Complete the following hypothesis test: Ho: μ = 7, Ha: μ < 7, α = 0.05. 6.6 7.8 7.9 6.3 6.9 5.3 7.8 5.9 6 7.4

(a) Find t. (Give your answer correct to two decimal places.)

______-0.72____

(ii) Find the p-value. (Give your answer correct to four decimal places.)

____________0.2449

(b) State the appropriate conclusion. (choose one) a) Reject the null hypothesis, there is not significant evidence that the mean is less than 7. b) Reject the null hypothesis, there is significant evidence that the mean is less than 7. c) Fail to reject the null hypothesis, there is not significant evidence that the mean is less than 7. d) Fail to reject the null hypothesis, there is significant evidence that the mean is less than 7.

Ans (b)

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