Final Answer:
1) Based on the given sample data, we reject the null hypothesis and conclude that there is sufficient evidence at the 5% level of significance to support the claim that international movies have a mean running time of more than 110 minutes.
2) At a 0.01 significance level, the data provides enough evidence to reject the null hypothesis, indicating that the mean systolic blood pressure of vegetarians is indeed lower than that of nonvegetarians.
Step-by-step explanation:
1) In the first scenario, we perform a one-sample t-test for the mean running time of international movies. The null hypothesis
assumes that the mean running time is 110 minutes or less, while the alternative hypothesis
suggests that it is more than 110 minutes. Using the given sample mean
, sample standard deviation (s = 7), sample size (n = 70), and a significance level of 0.05, we calculate the t-statistic and compare it to the critical value. With a t-statistic greater than the critical value, we reject the null hypothesis.
2) For the comparison of systolic blood pressure between vegetarians and nonvegetarians, a two-sample t-test is employed. The null hypothesis
posits that there is no difference in mean blood pressure, while the alternative hypothesis
suggests that the mean blood pressure of vegetarians is lower. Utilizing the provided sample means
,
, sample standard deviations
, and sample sizes
, along with a significance level of 0.01, we calculate the t-statistic and compare it to the critical value. The obtained t-statistic supports the rejection of the null hypothesis.
In both cases, the rejection of the null hypothesis implies that there is enough statistical evidence to support the respective claims at the specified significance levels.