MATH AP-A 95% confidence interval for a population mean is

MATH AP-A 95% confidence interval for a population mean is

Subject: Mathematics    / Statistics
Question
1.

A 95% confidence interval for a population mean is (28, 35).

a) Can you reject the null hypothesis that µ= 34 at the 5% significance level? Why?
b) Can you reject the null hypothesis that µ= 36 at the 5% significance level? Why?

2.

The P-value for a two-sided test of the null hypothesis is 0.06.

a) Does the 95% confidence interval include the value 10? Why?
b) Does the 90% confidence interval include the value 10? Why?

3.

An understanding of cockroach biology may lead to an effective control strategy for these annoying insects. Researchers studying the absorption of sugar by insects feed cockroaches a diet containing measured amounts of a particular sugar. After 10 hours, the cockroaches are killed and the concentration of the sugar in various body parts is determined by a chemical analysis. The paper that reports the research states that a 95% confidence interval for the mean amount (in milligrams) of the sugar in the hindguts of the cockroaches is 4.2±2.3.

a) Does this paper give evidence that the mean amount of sugar in the hindguts under these conditions is not equal to 7 mg? State and base a test on the confidence interval.
b) Would the hypothesis that µ = 5 mg be rejected at the 5% level in favor of a two-sided alternative