Question

A manufacturer of sprinkler systems used in office buildings to protect against fires claims that its sprinklers are activated at a temperature of 130°F. The sample of 9 systems recorded the temperature at the time of activation of the system.

Temperature 133.90 132.15 130.23 129.23 133.45 131.94 130.18 130.82 129.77

Summary Statistics

Mean: 131.29667

Std Dev: 1.6496212

Std. Err

Mean: 05498737 N:9

a) Construct a 99% confidence interval for the mean temperature at activation. What does this interval mean?

b) Construct a 99% upper confidence interval for the mean temperature at activation.

c) What size sample is necessary to construct a 99% confidence interval with a margin of error of only 0.5°F?

d) Can you conclude the manufacturer’s claim is wrong? (Do a hypothesis test.) e) Can you trust the results from the statistical procedures in parts a through d? Are the results valid?

Answer 1

a) df = 9 - 1 = 8

At 99% confidence level, the critical value is t_0.005,8 = 3.355

The 99% confidence interval is

We are 99% confidence that the true mean temperature at activation is in the above confidence interval.

b) The 99% upper confidence interval is

c) Margin of error = 0.5

d)

The test statistic is

At alpha = 0.005, the critical values are +/- t_0.005,8 = +/- 3.355

Since the test statistic value is not greater than the upper critical value, so we should not reject the null hypothesis.

No, we cannot conclude that the manufacturer's claim is wrong.

e) Yes, we can trust the results from the statistical procedures in parts a through d . Yes, the results are valid.