# Statistics: Hypothesis Testing Problem

1. The mean construction time for a standard two-car garage by Arrowhead Construction Company is 3.5 days. The time for the construction process follows the normal distribution. The construction process is modified through the use of 'precut and assembled roof trusses' rather than onsite construction of roof rafters. This should shorten the construction time. A sample of 15 garages had a mean time of 3.40 days with a standard deviation of 0.8 days. Does use of the "precut and assembled roof trusses' decrease the construction time? follow the hypothesis testing procedure using the 0.05 significance level by answering the following parts.

a) State the null and alternate hypotheses

b) State the decision rule

c) Compute the value of the test statistic

d) What is your decision regarding the null hypothesis?

2. The producer of a TV special expected about 40 percent of the viewing audience to watch a rerun of a 1965 Beatles concert. A sample of 200 homes revealed 60 to be watching the concert. At the 0.10 significance level. Does the evidence suggest that less than 40 percent were watching? Use the usual Hypothesis testing format.

a. state the null and alternate hypotheses

b. state the decision rule

c. compute the value of the test statistic

d. what is your decision regarding the null hypotheses

3A. A survey of 4000 college graduate determines that the mean length of time to earn a bachelor's degree is 5.08 years and the standard deviation is 1.89 years. Construct a 96 percent confidence interval for the mean time required for all graduates to earn a bachelor's degree.

B) A manufacturer of diamond drill bits for industrial production drilling and machining wishes to investigate the length of time a drill bit will last while drilling carbon steel. The production of the drill bits is very expensive, thus the number available for testing is small. A sample of 8 drill bits had a mean drilling time of 2.25 hours with a standard deviation of 0.5 hours. Construct a 95 percent confidence interval for the population mean. Is it reasonable for the manufacturer to claim that the drill bits will last 2.5 hours?

4. It was found that the mean length of 100 parts produced by a lathe was 20.05 mm with a standard deviation of 0.02mm.

Find the probability that a part selected at random would have a length

a) between 20.03 mm and 20.08 mm

b) between 20.06 mm and 20.07 mm

c) less than 20.01 mm

d) greater that 20.09 mm

5. The NPC, Inc. is a large mail order company that ships men's shirts all over the United States and Canada. They ship a large number of packages from their warehouse in Delta, Ohio. Their goal is to have 95 percent of the shipments delivered in 4 days. For many years they have used Brown Tuck Inc., but recently there have been complaints about slow and inconsistent delivery. A sample of 10 recent shipments handled by Brown Truck showed a standard deviation in delivery time of 1.25 days. A sample of 16 shipments by Rapid Package Service showed a standard deviation in their delivery time of 0.45 days. At the 0.05 significance level is there more variation in the Brown Truck delivery time?

Answer the following questions.

a)-State the null and alternate hypotheses

b)-State the decision rule

c)-Compute the value of the test statistic

d)-What is your decision regarding the null hypothesis? Interpret the result

#### Solution Preview

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1. The mean construction time for a standard two-car garage by Arrowhead Construction Company is 3.5 days. The time for the construction process follows the normal distribution. The construction process is modified through the use of 'precut and assembled roof trusses' rather than onsite construction of roof rafters. This should shorten the construction time. ...

#### Solution Summary

This solution provides a detailed explanation and computation of the given hypothesis testing questions.