Topic 5 - Hypothesis testing - single mean and proportion

Question 1

A telephone company claims that the mean duration of all long-distance phone calls made by its residential customers is 10 minutes. A random sample of 100 long-distance calls made by its residential customers taken from the records of this company showed that the mean duration of calls for this sample is 9.20 minutes. The population standard deviation is known to be 3.80 minutes. Use 2% significance level to test that the mean duration of all long-distance calls made by residential customers is different from 10 minutes. 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.Calculate the p-value.

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

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

Question 2

A soft-drink manufacturer claims that its 12-ounce cans do not contain, on average, more than 30 calories. A random sample of 64 cans of this soft drink, which were checked for calories, contained a mean of 32 calories with a standard deviation of 3 calories. Assume that the distribution of the calories of the soft drink is normally distributed. Use 5% significance level to determine that the mean calories in the soft drink is not more than 30 calories. 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

Question 3

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.