Question 980611: Assume that a simple random sample has been selected from a normally distributed population and test the given claim.
Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test
statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the
original claim.
Use a significance level of = 0.05 to test the claim that μ = 32.6. The sample data consist of
15 scores for which x = 42.5 and s = 5.9. Use the traditional method of testing hypotheses.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! alpha = 0.05
xbar = 42.5
s = 5.9
n = 15
df = n-1 = 15 - 1 = 14
We will use the T distribution because n > 30 is not true and we don't know sigma.
Hypothesis:
H0: mu = 32.6
H1: mu =/= 32.6
Claim is in the null hypothesis H0. This is a two tailed test. The null will be rejected if the test statistic is not between the critical values.
Test Statistic:
t = (xbar - mu)/(s/sqrt(n))
t = (42.5 - 32.6)/(5.9/sqrt(15))
t = 6.49873476736499
t = 6.4987
Critical Values (alpha = 0.05, df = 14)
Use a table like this one to find the critical values to be -2.145 and 2.145
The test statistic 6.4987 is NOT between the critical values -2.145 and 2.145. So we reject the null hypothesis. There is enough statistically significant evidence to reject the null.
This means that the population mean mu is NOT 32.6. The initial claim is false.
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