# Confidence interval and Hypothesis testing problems

1) The length of time to do a complete full service oil change at Speedy-Lube, is normally distributed with a mean of 15.8 minutes and a standard deviation of 2.2 minutes.

Refer to the following table.

Table 5A Below

normal distribution

p(lower)

p(upper) z x mean std.dev

.0042 .9958 -2.64 10 15.8 2.2

.9719 .0281 1.91 20 15.8 2.2

.1016 .8984 -1.27 13 15.8 2.2

.8413 .1587 1.00 18 15.8 2.2

Part A:

Analyze the output above to determine what percentage of complete full service oil changes will fall between 13 and 20 minutes?

Part B

What percentage of complete full service oil changes will take less than 10 minutes? If 1000 cars had a complete full service oil change, how many would you expect to be finished in less than 10 minutes?

2) The length of time to do a cable installation by Multi-cable Inc is normaly distributed with a mean of 42.8 minutes and a standard deviation of 6.2 minutes.

p(lower)

p(upper) z x mean std.dev

.9000 .1000 1.28 50.75 42.8 6.2

.7500 .2500 0.67 46.98 42.8 6.2

.8000 .2000 0.84 48.02 42.8 6.2

.1000 .9000 -1.28 34.85 42.8 6.2

.2500 .7500 -0.67 38.62 42.8 6.2

.2000 .8000 -0.84 37.58 42.8 6.2

Multi cable wants to establish how long a standard cable install appointment should be to insure that all of the work will be completed during the appointment 75% of the time. How long would you recommend the standard cable installation appointment be?

3) You are in charge of selling advertising for radio station KGSM. The fee you can set for air time is directly related to the share of the listening market your station reaches. From time to time you conduct surveys to determine KGSM;s share of the market. This month when you contacted 200 randomly selected residential phone numbers, 12 respondents said they listen to KGSM.

Table 7A Below

Confidence interval - proportion

99% confidence level

0.06 proportion

200 n

2.576 z

0.043 half-width

0.103 upper confidence limit

0.017 lower confidence limit

Part A

What is the 99% confidence interval for the percentage of the market that are listeners of KGSM. Interpret this confidence level.

Part B

A KGSM sales person tells potential advertisers that KGSM has a 10% share. What would you tell this salesperson? ( is the sales person correct? whY?

4) GE fluorescent bulbs have a useful lifetime which is normally distributed. We wish to estimate mean lifetime. A random sample of 20 bulbs yields the following results: sample mean = 2,360 hours and a sample standard deviation of 365 hours.

Refer to table:

Table 8B Below

Confidence interval - mean

95% confidence level

2360 mean

365 std. dev.

20 N

2.093 t (df = 19)

170.825 half-width

2530.825 upper confidence limit

2189.175 lower confidence limit

Part A

Analyze the output above to determine the 95% confidence interval for the mean lifetime of GE fluorescent bulbs. Interpret this confidence interval

Part B

Suppose a GE executive says, "our fluorescent bulbs have an average expected life of 2500 hours? Could the executive be correct?

#### Solution Summary

Step by step method for testing the hypothesis under 5 step approach is discussed here. Construction of confidence interval for population mean is also discussed in the answer. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.