# Hypothesis Testing of Mean & Proportion

Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, µ spent by customers at the supermarkets has been reported to be 35 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that µ is greater than 35 minutes .

To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 40 minutes and the standard deviation of the times to be 12 minutes.

What are the null hypothesis ( Ho ) and the alternate hypothesis( H1) that should be used in the test?

In the context of this test, what is the type II error?

A type II error is __________________the hypothesis that is µ is ________when, in fact, µ is___________

Suppose the consultant decides to reject the null hypothesis. What type of error might she be making?

One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score, µ, among the general population on this subsection. The website reports that µ is 140, but you believe that µ is greater than 140. You decide to do a statistical test. You choose a random sample of people and have them take the personality test. You find that their mean score on the subsection is 145 and that the standard deviation of their scores is 25.

What are the null hypothesis ( Ho ) and the alternate hypothesis( H1) that should be used in the test.?

In the context of this test, what is the type I error?

A type 1 error is __________________the hypothesis that is µ is ________when, in fact, µ is___________

Suppose the consultant decides to reject the null hypothesis. What type of error might she be making?

A furniture store claims that a specially ordered product will take, on average, µ = 35 days (5 weeks) to arrive. The standard deviation of these waiting times is 6 days. We suspect that the special orders are taking longer than this. To test this suspicion, we track a random sample of 90 special orders and find that the orders took a mean of 36 days to arrive. Can we conclude at the 0.1 level of significance that the mean waiting time on special orders at this furniture store exceeds 35 days

Perform a one-tailed test

Null Hypothesis: Ho

Alternative Hypothesis: H1

Type of Test Statistic:

The Value of the Test Statistic:

The p-value:

Can we compute that the mean waiting time on special orders at this furniture store exceeds 35 days?

A coin-operated drink machine was designed to discharge a mean of 6 ounces of coffee per cup. In a test of the machine, the discharge amounts in 20 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 6.13 ounces and 0.23 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.05 level of significance, to conclude that the true mean discharge, µ, differs from 6 ounces?

Perform a one-tailed test

Null Hypothesis: Ho

Alternative Hypothesis: H1

Type of Test Statistic:

The Value of the Test Statistic:

The two critical values at the 0.05 level of significance.

At the 0.05 level of significance, can we conclude that the true mean discharge differs from 6 ounces?

A decade-old study found that the proportion, p , of high school seniors who believed that "getting rich" was an important personal goal was 80%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 235 high school seniors in his random sample, 193 believe that "getting rich" is an important goal. Can he conclude, at the 0.05 level of significance, that the proportion has indeed changed?

Perform a two-tailed test

Null Hypothesis: Ho

Alternative Hypothesis: H1

Type of Test Statistic:

The Value of the Test Statistic:

The two critical values at the 0.05 level of significance

Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed?

#### 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.