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In: Statistics and Probability

Question 1. a) The P-value for a two-sided test of the null hypothesis H0: mu =...

Question 1.

a) The P-value for a two-sided test of the null hypothesis H0: mu = 30 is 0.08

i.) Does the 95% confidence interval include the value of 30? Explain.

ii.) Does the 90% confidence interval include the value of 30? Explain.

b) A 95% confidence for a population mean is (57,65)

i.) Can you reject the null hypothesis that mu = 68 at the 5% significance level? Explain.

ii.) Can you reject the null hypothesis that mu = 62 at the 5% significance level? Explain.

c) The P-value for a significance test is 0.026

i.) Do you reject the null hypothesis at level alpha = 0.05? Explain.

ii.) Do you reject the null hypothesis at level alpha = 0.01? Explain.

d) What critical value t* should be used to calculate the margin of error for a confidence interval for the mean of the population in each of the following situations? [Hint: To determine the t critical value, we use a t critical value table or calculator. The table/calculator/function uses two values, the significance level and the degree of freedom. The significance level is 100% – 95% = 5% or 0.05. The degree of freedom is n – 1 = 14.]

i.) A 95% confidence interval based on n=15 observations.

ii.) A 95% confidence interval based on n=25 observations.

iii.) A 90% confidence interval based on n=25 observations.

iv.) A 95% confidence interval based on n=101 observations.

e.) The cases in question d) illustrate how the size of the margin of error depends upon the confidence level and sample size. Summarize these relationships.

Expert Solution

orchestra answered 2 years ago

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