9.6 Please explain the Steps and show how you managed to arrive on the following

Question

9.6

Please explain the Steps and show how you managed to arrive on the following solutions. as this is also me trying to learn

9.6 A random sample of n = 35 observations from a quantitative population produced a mean x = 2.4 and a standard deviation s = 0.29. Suppose your research objective is to show that the population mean exceeds 2.3 a. Give the null and alternative hypotheses for the test. b. Locate the rejection region for the test using a 5% significance level. c. Find the standard error of the mean. d. Before you conduct the test, use your intuition to decide whether the sample mean x = 2.4 is likely or unlikely, assuming that = 2.3. Now conduct the test. Do the data provide sufficient evidence to indicate that > 2.3?

Explanation / Answer

a)

H0 : the population mean doesnt exceed 2.3

H1 : the population mean exceeds 2.3

b)

we have n = 35 , so df = n-1 = 34 and alpha = 0.05 for 1 tail we check the critical value as 1.69

c) the standard error of the mean is

sigma/sqrt(n)

0.29/sqrt(35) = 0.049

d)

we conduct the t test as

t = (xbar-mean)/(sd/sqrt(n))

t = (2.4-2.3)/(0.29/sqrt(35) = 2.04

as the t stat is greater than t critical  1.69 , hence we reject the null hypothesis in favor of alternate hypothesis

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