Exam 9: Estimation and Confidence Intervals

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 25 randomly selected recent graduates yielded a mean of $52,000. What is the value of The sample test statistic?

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?

If α = 0.05, what is the probability of making a Type I error?

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 your decision if α = 0.01?

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 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. Does this sample support the original claim? What is the decision for a statistical significant change in average weights at birth at the 5% level of Significance?

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?

The average cost of tuition, room and board at community colleges is reported to be $8,500 per Year with a standard deviation of $1,200, 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. Let α = 0.05. What is the critical z-value for this test?

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. Hypothesis testing is a procedure based on sample evidence and probability theory to decide Whether the hypothesis is a reasonable statement. iii. 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.

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.

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.

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.

The null hypothesis makes a claim about what 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.

A machine is set to fill the small-size packages of Smarties candies with 56 candies per bag. A Sample revealed: four bags of 56, two bags of 57, one bag of 55, and two bags of 58. To test the Hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?

A random sample of size 15 is selected from a normal population. The population standard deviation Is unknown. Assume that a two-tailed test at the 0.10 significance level is to be used. For what value Of t will the null hypothesis be rejected?

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 following megastat printout, explain the meaning of the p-value.

i. If the null hypothesis is μ ≥ 200 and the alternate hypothesis states that μ is less than 200, then, a Two-tail test is being conducted. ii. For a one-tailed test of hypothesis, the area of rejection is only in one tail of the curve. iii. As the sample size increases, the curve of the t-distribution approaches the standard normal Distribution

For a two-tailed test at the 0.05 significance level, what is the rejection region when the population Standard deviation is known?