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# Hypothesis testing problems

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1. Sandy's Pizza has generally assumed that the mean age of its customers was 30 years of age or younger. A random sample of 50 customers revealed the following:

X-bar=30.76 years and s=3.6 years

Does the sample data provide sufficient evidence to conclude that the mean age of Sandy's customers is greater than 30 years (using alpha=.05)? In answering this question be sure to address all of the points below.
a. State the null and alternative hypothesis

b. State the level of significance

c. Find the critical value (or values) and clearly show the rejection and non-rejection regions

d. Compute the test statistic

e. Decide whether you can reject Ho and Accept Ha or not.

f. Explain and interpret your conclusion in part e.

g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?

h. Does the sample data provide evidence (alpha=.05), that the mean age of Sandy's customers is indeed over 30?

2. The manager of accounts receivables believes that less than 10% of invoices have at least one error. A random sample of 400 invoices yields 30 invoices with at least one error. Does the sample data provide evidence to support the manager's claims(using alpha - .10)? In answering this question be sure to address all of the points below.
a. State the null and alternative hypothesis?

b. State the level of significance.

c. Find the critical value or values and clearly show the rejection and non-rejection regions

d. Compute the test statistic

e. Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e.

g. Determine the observed p-valuefor the hypothesis test and interpret this value. What does this mean?

h. Does the sample data provide evidence (alpha = .10) , that less than 10% of invoices have at least one error.

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