Exam 9: One-Sample Tests of Hypothesis

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.

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 an increase in the weekly production of the Model A325 desk. The mean number of desks produced last year (50 weeks, because the plant was shut down two weeks for vacation) is 203.5. Is the mean number of desks increased from 200? Test using the.01 significance level.

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample standard deviation?

The following summarizes the average of the TSE 300 Index at the end of 20 randomly selected weeks in 2000. Using a 5% level of significance, can it be agreed that the Index average was more than $9,600 during the year 2000?

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 16.9. A random sample of 16 items results in a sample mean of 17.8 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.

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 different from $19.50?

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the alternate hypothesis for a one-sided test?

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? The mean number of desks produced last year (50 weeks, because the plant was shut down two weeks for vacation) is 203.5. Test using the.01 significance level. i. The alternate hypothesis is $\mu$ $\neq$ 200. ii. It is appropriate to use the z-test. 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.

The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. Has there been a statistically significant change in the mean length of the bars?

The mean gross annual incomes of certified tack welders are normally distributed with the mean of $50,000 and a standard deviation of $4,000. The ship building association wishes to find out whether their tack welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. Given the following megastat printout, what conclusions can be made?

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 20 randomly selected recent graduates yielded a mean of $55,000. What is the value of the sample test statistic?

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. Test at the 5% level of significance.

One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire. The warranty is for 40,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A sample 49 tires revealed that the mean number of miles is 45,000 miles with a standard deviation of 15,000 miles. Test the hypothesis with a 0.05 significance level.

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 $52,000. What is the value of the sample test statistic?

If $\alpha$ = 0.05 for a two-tailed test, how large is the acceptance area?

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample variance?

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 your decision if $\alpha$ = 0.01?

i. To prevent bias, the level of significance is selected before setting up the decision rule and sampling the population. ii. The level of significance is the probability that a true hypothesis is rejected. iii. If the critical values of the test statistic z are $\pm$ 1.96, they are the dividing points between the areas of rejection and non-rejection.

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 16.9. A random sample of 25 items results in a sample mean of 17.8 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.

i. Two types of possible errors always exist when testing hypotheses-a Type I error, in which the null hypothesis is rejected when it should not have been rejected, and a Type II error in which the null hypothesis is not rejected when it should have been rejected. ii. A test statistic is a value determined from sample information collected to test the null hypothesis. iii. If we do not reject the null hypothesis based on sample evidence, we have proven beyond doubt that the null hypothesis is true.