Exam 9: One-Sample Tests of a Hypothesis

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?

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. If α = 0.025, what will be the 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 sample proportion?

What are the two rejection areas in using a two-tailed test and the 0.01 level of significance when n is large?

What are the two rejection areas in using a two-tailed test and the 0.01 level of significance when n is large?

A machine is set to fill the small size packages of Smarties candies with 56 candies per bag. A sample revealed: 3 bags of 56, 2 bags of 57, 1 bag of 55, and 2 bags of 58. How many degrees of freedom are there?

i. The standard normal distribution is the appropriate distribution when testing a hypothesis about a population proportion. Ii) When testing population proportions, the z statistic can be used when np and n(1 - p) are greater than five. Iii) To conduct a test of proportions, the assumptions required for the binomial distribution must be met.

What does z equal for an α = 0.01 and a lower level test?

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.

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 18.0 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 your decision if α = 0.01?

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?

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?

The average cost of tuition, room and board at community colleges is reported to be $8,500 per year, but a financial administrator believes that the average cost is higher. A study conducted using 150 community colleges showed that the average cost per year is $9,000 with a standard deviation of $1,200. Let α = 0.05. Given the z-statistic is 5.1, what is our decision about the average cost?

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 -2.58 and the level of significance is 0.02, what is your decision?

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. The region or area of rejection defines the location of all those values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.

The average cost of tuition, room and board at community colleges is reported to be $8,500 per year, but a financial administrator believes that the average cost is higher. A study conducted using 150 community colleges showed that the average cost per year is $9,000 with a standard deviation of $1,200. Let α = 0.05. What are the null and alternative hypotheses for this study?

i. For a one-tailed test using the 0.05 level of significance, the critical value for the z test is 1.645, but for t it is 1.96. Ii) For a one-tailed test using the 0.01 level of significance, the critical value for the z-test is 1.645, but for t it is 1.96. Iii) For a two-tailed test using the 0.05 level of significance the critical value for the z-test is 1.96 and it is the same for the t-test.

If the 1% level of significance is used and the computed value of z is +6.00, what is our decision?

What is a Type II error?