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Chapter 9: Q. 9.81 (page 380)
We have been provided a sample mean, sample size, and population standard deviation. In the given case, use the one-mean z-test to perform the required hypothesis test at the significance level.
The value of z is , critical value isand do not reject.
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The following graph portrays the decision criterion for a onemean z-test, using the critical-value approach to hypothesis testing. The curve in the graph is the normal curve for the test statistic under the assumption that the null hypothesis is true.
Determine the
a. rejection region.
b. nonrejection region.
c. critical value(s).
d. significance level.
e. Draw a graph that depicts the answers that you obtained in parts (a)-(d).
f. Classify the hypothesis test as two tailed, left tailed, or right tailed.
Beef Consumption. According to Food Consumption, Prices,\and Expenditures, published by the U.S. Department of Agriculture. the mean consumption of beef per person in 2011 was 57.5 lb. A sample of 40 people taken this year yielded the data, in pounds, on last year's beef consumption given on the Weiss Stats site. Use the technology of your choice to do the following.
a. Obtain a normal probability plot, a boxplot, a histogram, and a stem-and-leaf diagram of the data on beef consumptions.
b. Decide, at the 5% significance level, whether last year's mean beef consumption is less than the 2011 mean of 57.5 lb. Apply the one mean t-test.
c. The sample data contain four potential outliers: 0, 0, 0, and 13.Remove those four observations, repeat the hypothesis test in part (b), and compare your result with that obtained in part (b).
d. Assuming that the four potential outliers are not recording errors, comment on the advisability of removing them from the sample data before performing the hypothesis test.
e. What action would you take regarding this hypothesis test?
9.93 Cell Phones. The number of cell phone users has increased dramatically since . According to the Semi-annual Wireless Survey, published by the Cellular Telecommunications & Internet Association, the mean local monthly bill for cell phone users in the United States was in . Last year's local monthly bills, in dollars, for a random sample of cell phone users are given on the WeissStats site. Use the technology of your choice to do the following.
a. Obtain a normal probability plot, boxplot, histogram, and stemand-leaf diagram of the data.
b. At the significance level, do the data provide sufficient evidence to conclude that last year's mean local monthly bill for cell phone users decreased from the mean of Assume that the population standard deviation of last year's local monthly bills for cell phone users is .
c. Remove the two outliers from the data and repeat parts (a) and (b).
d. State your conclusions regarding the hypothesis test.
As we mentioned on page 378, the following relationship holds between hypothesis test and confidence intervals for one-mean z-procedures: For a two-tailed hypothesis test at the significance level , the null hypothesis role="math" localid="1653038937481" will be rejected in favor of the alternative hypothesis if and only if lies outside the -level confidence interval for . In each case, illustrate the preceding relationship by obtaining the appropriate one-mean z-interval and comparing the result to the conclusion of the hypothesis test in the specified exercise.
Part (a): Exercise 9.84
Part (b): Exercise9.87
The normal probability curve and stem-and-leaf diagram of the data are shown in figure; is known.
Perform Hypothesis test for mean of the population from which data is obtained and decide whether to use z-test, t-test or neither. Explain your answer.
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