Exam 9: One-Sample Tests of a Hypothesis

i. If the critical values of the test statistic z are ±1.96, they are the dividing points between the areas of rejection and non-rejection. Ii) The probability of a Type I error is also referred to as alpha. Iii) A Type I error is the probability of accepting a true null hypothesis.

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. If the level of significance is 0.10, what is the critical value?

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 is the critical z-value for this 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. What is the alternate hypothesis for a one-sided test?

What is the probability of making a Type II error if the null hypothesis is actually true?

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. The first step in testing a hypothesis is to state the decision rule. ii. To prevent bias, the level of significance is selected before setting up the decision rule and sampling the population. Iii) 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.

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

Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 35,600 kilometres. A manufacturer of spark plugs claims that its plugs have an average life in excess of 35,600 kilometres. The fleet owner purchased 18 sets and found that the sample average life was 37,700 kilometres, the sample standard deviation was 2415 kilometres and the computed t = 3.677.

i. To set up a decision rule, the sampling distribution is divided into two regions-a region of non- rejection and a region where the null hypothesis is rejected. Ii) A test statistic is a value determined from sample information collected to test the null hypothesis. iii. If the null hypothesis is true and the researchers do not reject it, then a correct decision has been made.

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 z-statistic?

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

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. What is the sample variance?

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.

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?

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?

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.

Which of the following is a test statistic used to test a hypothesis about a population?

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? What is the alternate hypothesis?