Exam 9: One-Sample Tests of Hypothesis

The Jamestown Steel Company manufactures and assembles desks and other office equipment at several plants. The weekly production of the Model A325 desk follows a normal probability distribution, with a mean of 200 and a standard deviation of 16. Recently, due to market expansion, new production methods have been introduced and new employees hired. The vice president of manufacturing would like to investigate whether there has been a change in the weekly production of the Model A325 desk. Is the mean number of desks produced different from 200? Test using the.01 significance level. The mean number of desks produced last year (50 weeks, because the plant was shut down two weeks for vacation) is 203.5. i. The alternate hypothesis is $\mu$ $\neq$ 200. ii. The calculated value of z is 1.55. iii. The decision rule is: if the computed value of the test statistic is not between -2.58 and 2.58, reject the null hypothesis.

Which of the following is NOT one of the five steps in the hypothesis testing procedure?

i. The fifth and final step in testing a hypothesis is taking a sample and, based on the decision rule, deciding if the null hypothesis should be rejected. ii. When the null hypothesis is not rejected, the conclusion is that our sample data does not allow us to reject the null hypothesis. iii. The level of significance is selected after setting up a decision rule and sampling the population.

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the computed value of z = -2.25 and the level of significance is 0.03, what is your decision?

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the critical value if the level of significance is 0.10?

What must both np and n(1 - p) exceed in testing a hypothesis involving one proportion?

What are the critical z-values for a two-tailed hypothesis test if $\alpha$ = 0.01?

The null hypothesis makes a claim about what value?

i. An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected. ii. The level of significance is the risk we assume of rejecting the null hypothesis when it is actually true. iii. The researcher must decide on the level of significance before formulating a decision rule and collecting sample data.

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is -2.054 and the level of significance is 0.03, what is your decision?

i. Two examples of a hypothesis are: 1) mean monthly income from all sources for senior citizens is $841 and 2) twenty percent of juvenile offenders ultimately are caught and sentenced to prison. ii. Since there is more variability in sample means computed from smaller samples, we have more confidence in the resulting estimates and are less apt to reject null hypothesis. iii. We call a statement about the value of a population parameter a hypothesis.

The dean of a business school claims that the average starting salary of its graduates is more than $50,000. It is known that the population standard deviation is $10,000. Sample data on the starting salaries of 36 randomly selected recent graduates yielded a mean of $62,000. What is the value of the sample test statistic?

i. A sample proportion is found by dividing the number of successes in the sample by the number sampled. ii. The standard normal distribution is the appropriate distribution when testing a hypothesis about a population proportion. iii. When testing population proportions, the z statistic can be used when np and n(1 - p) are greater than five.

The printout below refers to the weekly closing stock prices for Air Canada on 20 randomly selected weeks in 2000. Using a 5% level of significance, can you say that the average Air Canada stock price was less than $19.50?

i. A sample proportion is found by dividing the number of successes in the sample by the number sampled. ii. The standard normal distribution is the appropriate distribution when testing a hypothesis about a population proportion. iii. To conduct a test of proportions, the assumptions required for the binomial distribution must be met.

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218 and 218. At the 0.025 level, has the shelf life of the cake mix increased?

A nationwide survey of college students was conducted and found that students spend two hours per class hour studying. A professor at your school wants to determine whether the time students spend at your school is significantly different from the two hours. A random sample of fifteen statistics students is carried out and the findings indicate an average of 1.75 hours with a standard deviation of 0.24 hours. Given the following printout, what can you determine?

What is a Type II error?

What is the critical z-value for a one-tailed lower test at the 1% level of risk?

Using a 5% level of significance and a sample size of 25, what is the critical t value for a null hypothesis, H₀:µ $\le$ 100?