Exam 9: One-Sample Tests of a Hypothesis

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 6.9. A random sample of 25 items results in a sample mean of 17.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.

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?

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 alternate hypothesis?

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 α = 0.01?

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?

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?

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 z-statistic?

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of significance. The t-value is calculated to be 5.77. At the 0.01 level of significance, what is your decision?

If the alternate hypothesis states that μ does not equal 4,000, what is the rejection region for the hypothesis test?

For a one-tailed hypothesis test, the critical z-value of the test statistic is -2.33. Which of the following is true about the hypothesis test?

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.

What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 25?

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 null hypothesis?

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.

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.

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 6.9. 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.

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 null hypothesis?

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) There is only one level of significance that is applied to all studies involving sampling.

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 sample proportion?

The mean weight of newborn infants at a community hospital is 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. Does this sample support the original claim? The null hypothesis is: