Question

Question 11 A group of 50 college students from a certain liberal arts college were Type numbers in the boxes. randomly sampled and asked about the number of alcoholic drinks they have 10 points in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73. The group of 50 students in the study reported an average of 4.21 drinks per with a standard deviation of 3.43 drinks. Find the p-value for the hypothesis test. The p-value should be rounded to 4-decimal places. Question 12 Commute times in the U.S. are heavily skewed to the right. We select a Type numbers in the boxes. random sample of 490 people from the 2000 U.S. Census who reported a non- 10 points zero commute time. In this sample, the mean commute time is 28.3 minutes with a standard deviation of 18.7 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance. What is the p-value for this hypothesis test? | (Your answer should be rounded to 4 decimal places.)

Answer 1

11)
Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 4.73
Alternative Hypothesis: μ ≠ 4.73

Rejection Region
This is two tailed test, for α = 0.05 and df = 49
Critical value of t are -2.01 and 2.01.
Hence reject H0 if t < -2.01 or t > 2.01

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (4.21 - 4.73)/(3.43/sqrt(50))
t = -1.072

P-value Approach
P-value = 0.2890

12)
Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 30
Alternative Hypothesis: μ < 30

Rejection Region
This is left tailed test, for α = 0.05 and df = 489
Critical value of t is -1.648.
Hence reject H0 if t < -1.648

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (28.3 - 30)/(18.7/sqrt(490))
t = -2.012

P-value Approach
P-value = 0.0224