Exam 9: One-Sample Tests of 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.

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 $18.00?

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?

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 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.

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 decision rule?

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

Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is p = 0.55 and the alternate is p $\neq$ 0.55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null 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.

What is the critical value for t in a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 15?

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 mean?

From past records it is known that the average life of a battery used in a digital clock is 305 days. The battery life is normally distributed. The battery was recently modified to last longer. A sample of 20 of the modified batteries was tested. It was discovered that the mean life was 311 days and the sample standard deviation was 12 days. We want to test at the 0.05 level of significance whether the modification increases the life of the battery. What is our decision rule?

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 alternate hypothesis?

i. One assumption in testing a hypothesis about a proportion is that the data collected are the result of counting something. ii. One assumption in testing a hypothesis about a proportion is that an outcome of an experiment can be classified into two mutually exclusive categories, namely, a success or a failure. iii. A proportion is a fraction, ratio or probability that gives the part of the population or sample that has a particular trait of interest.

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?

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 critical value for $\alpha$ = 0.025?

i. 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. 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.

i. To prevent bias, the level of significance is selected before setting up the decision rule and sampling the population. ii. 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. iii. When the null hypothesis is not rejected, the conclusion is that our sample data does not allow us to reject the null 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 alternate hypothesis?

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

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. The calculated value of z is 2.55. 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.