Chapter 8 Discussion

Consider the following hypotheses and statistical values with the sample mean daily wage for a random sample of 15 fast food workers of  x¯ = $102, and the sample standard deviation s = $4. A claim states that the mean daily wage is greater than $100. Testing at a significance level of 0.05, state the rejection rule and conclusion for p-value method and then for critical value method.

Hypotheses:        H0:  Î¼ = $100                             Degrees of Freedom:   15 – 1 = 14

H1:  Î¼ > $100                             Significance Level:        alpha = .05

Test Statistic:   t = (102–100)/(4/√15) = 1.936       Or shown in fraction form      t = 102−100415  = 1.936

Answer #1 – 4 below.

1.  Of the three sets of critical values here, choose the correct critical value of t to use in rejection rules:

Critical value of t for a 1-tail rejection area is:  t = 1.761       (found using table A-3)

Critical value of t for a 1-tail rejection area is:  t = -1.761     (found using table A-3)

Critical values of t for a 2-tail rejection area is:  t = ±2.145   (found using table A-3)

2.  Of the four p-values here, choose the correct p-value to use for rejection rules:

p-value for a 1-tail rejection area = P(t > 1.936) = .9633           (found using technology)

p-value for a 1-tail rejection area = P(t < -1.936) = .03667       (found using technology) 

p-value for a 1-tail rejection area = P(t > 1.936) = .03667        (found using technology)

p-value for a 2-tail rejection area = 2 *P(t > 1.936) = .07332     (found using technology)

3.  State the rejection rule and conclusion for the p-value method:

           Rejection rule:

           Conclusion:

4.  State the rejection rule and conclusion for the critical value method:

           Rejection rule:

           Conclusion:

Note: these are the same hypothesis test so the conclusion to reject H0 or not reject H0 will be the same for both. Hints provided for Excel Lab 5 (in the course announcements and in the link for Excel Lab 5 directions) explain rejection rules, study those hints.

For the rejection rule: include significance level in the p-value rejection rule and include critical value(s) in the critical value rejection rule.

For the conclusion write a complete sentence that explains whether you reject H0 or do not reject H0. Include the comparison of the p-value or critical value as needed and include the context of the data set. Use statistical language and symbols as needed.

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