According to a 2018 survey by a research group, 30% of adults typically run the water for a period of 6 to 10 minutes while taking the shower

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Question 1

According to a 2018 survey by a research group, 30% of adults typically run the water for a period of 6 to 10 minutes while taking the shower. Suppose that in a recent survey of 400 adults, 104 stated that they typically run the water for a period of 6 to 10 minutes when they take a shower. At the 5% significance level, can you conclude that the proportion of all adults run the water for a period of 6 to 10 minutes when they take a shower is less than 0.30? Answer the following questions.

i. Identify the claim and state the H0 and H1.

ii. Find the critical value.

iii. Calculate the test statistic.

iv. Make a decision to reject or fail to reject the H0.

v. Interpret the decision in the context of the original claim.

Hypothesis testing – comparing two means and proportion

Question 2

A local college cafeteria has a self-service soft ice cream machine. The cafeteria provides bowls that can hold up to 16 ounces of ice cream. The food service manager is interested in comparing the mean amount of ice cream dispensed by male students to the mean amount dispensed by female students. A measurement device was placed on the ice cream machine to determine the amounts dispensed. Random samples of 85 male and 78 female students who got ice cream were selected. The sample means were 7.23 and 6.49 ounces for the male and female students, respectively. Assume that the population standard deviations are 1.22 and 1.17 ounces, respectively. Use 1% significance level to determine that the average amount of ice cream dispensed by male college students is larger than the average amount dispensed by female college students. Answer the following questions.

Male student Female student

Mean sample 7.23 oz 6.49 oz

Population standard deviation 1.22 oz 1.17 oz

Sample size 85 78

i. Identify the claim and state the H0 and H1.

ii. Find the critical value.

iii. Calculate the test statistic.

iv. Make a decision to reject or fail to reject the H0.

v. Interpret the decision in the context of the original claim.

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