Exam 9: Estimation and Confidence Intervals

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?

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

Which of the following does NOT hold true for the t distribution?

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.

A manufacturer of stereo equipment introduces new models in the fall. Retail dealers are surveyed Immediately after the Christmas selling season regarding their stock on hand of each piece of Equipment. It has been discovered that unless 40% of the new equipment ordered by the retailers In the fall had been sold by Christmas, immediate production cutbacks are needed. The Manufacturer has found that contacting all of the dealers after Christmas by mail is frustrating as Many of them never respond. This year 80 dealers were selected at random and telephoned Regarding a new receiver. It was discovered that 38% of those receivers had been sold. Since 38% Is less than 40%, does this mean that immediate production cutbacks are needed or can this Difference of 2 percentage points be attributed to sampling? Test at the 0.05 level. Computed z = -0.37.

To conduct a test of hypothesis with a small sample, we need to be able to make the following Assumption that:

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?

i. A sample proportion is found by dividing the number of successes in the sample by the number Sampled. ii. The standard normal distribution is the appropriate distribution when testing a hypothesis about a Population proportion. iii. To conduct a test of proportions, the assumptions required for the binomial distribution must be met.

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. Given the following megastat printout, what conclusions can be made?

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. If α = 0.05, what is the critical t value?

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?

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 With a standard deviation of 15,000 miles. A sample 49 tires revealed that the mean number of Miles is 45,000 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 16.9. 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.

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.

i. If we do not reject the null hypothesis based on sample evidence, we have proven beyond doubt That the null hypothesis is true. 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 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 $52,000. What is the value of The sample test statistic?

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?

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.

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. The test statistic for a problem involving an unknown population standard deviation is the Student's t distribution.