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# Hypothesis Testing Problems

For each problem below, answer the following

1. State the Ho
2. State the H1
3. Find the critical value
4. Determine the test statistic. Explain
5. State the decision rule
6. Show the decision rule graphically
7. Determine the computed value of the test statistic
8. Determine the p-value
10. Interpret the decision

1. Tom Sevits is the owner of the Appliance Patch. Recently Tom observed a difference in the
dollar value of sales between the men and women he employs as sales associates. A sample
of 40 days revealed the men sold a mean of \$1,400 worth of appliances per day with a
standard deviation of \$200. For a sample of 50 days, the women sold a mean of \$1,500
worth of appliances per day with a standard deviation of \$250. At the .05 significance level
can Mr. Sevits conclude that the mean amount sold per day is larger for the women?

2. Of 150 adults who tried a new peach-flavored peppermint patty, 87 rated it excellent. Of 200
children sampled, 123 rated it excellent. Using the .10 level of significance, can we conclude
that there is a significant difference in the proportion of adults and the proportion of children
who rate the new flavor excellent?

3. The production manager at Bellevue Steel, a manufacturer of wheelchairs, wants to compare
the number of defective wheelchairs produced on the day shift with the number on the
afternoon shift. A sample of the production from 6 day shifts and 8 afternoon shifts revealed
the following number of defects.
Day 5 8 7 6 9 7
Afternoon 8 10 7 11 9 12 14 9
At the .05 significance level, is there a difference in the mean number of defects per shift?

4. Advertisements by Sylph Fitness Center claim that completing their course will result in
losing weight. A random sample of eight recent participants showed the following weights
before and after completing the course. At the .01 significance level, can we conclude the
students lost weight?

Name Before After
Hunter 155 154
Cashman 228 207
Mervine 141 147
Massa 162 157
Creola 211 196
Peterson 164 150
Redding 184 170
Poust 172 165

5. The Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies
for visitors to the Myrtle Beach area. There are two facilities, one in the Little River
Area and the other in Murrells Inlet. The Quality Assurance Department wishes to compare
the mean waiting time for patients at the two locations. Samples of the waiting times, reported
in minutes, follow:
Location Waiting Time
Little River 31.73 28.77 29.53 22.08 29.47 18.60 32.94 25.18 29.82 26.49
Murrells Inlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.10 26.69 22.31

At the .05 significance level, is there a difference in the mean waiting time?

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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