| № |
Condition |
free/or 0.5$ |
| m6788 | A random sample of 150 residents in one community was asked to indicate their first preference for one of three television stations that air the 5 p.m. news. The results obtained are shown in the following table. Test the null hypothesis that for this population their first preferences are evenly distributed over the three stations. |
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| m6789 | A random sample of 1,556 people in country A were asked to respond to this statement: Increased world trade can increase our per capita prosperity. Of these sample members, 38.4% agreed with the statement. When the same statement was presented to a random sample of 1,108 people in country B, 52.0% agreed. Test the null hypothesis that the population proportions agreeing with this statement were the same in the two countries against the alternative that a higher proportion agreed in country B. |
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| m6790 | A random sample of 156 grade point averages for students at one university is stored in the data file Grade Point Averages.
a. Compute the first and third quartiles.
b. Calculate the 30th percentile.
c. Calculate the 80th percentile. |
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| m6791 | A random sample of 1,562 undergraduates enrolled in management ethics courses was asked to respond on a scale from 1 (strongly disagree) to 7 (strongly agree) to this proposition: Senior corporate executives are interested in social justice. The sample mean response was 4.27, and the sample standard deviation was 1.32.
Test at the 1% level, against a two-sided alternative, the null hypothesis that the population mean is 4. |
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| m6792 | A random sample of 1,562 undergraduates enrolled in management ethics courses was asked to respond, on a scale from 1 (strongly disagree) to 7 (strongly agree), to this proposition: Senior corporate executives are interested in social justice. The sample mean response was 4.27, and the sample standard deviation was 1.32.
a. Test at the 1% level, against a two-sided alternative, the null hypothesis that the population mean is 4.
b. Find the probability of a 1%-level test accepting the null hypothesis when the true mean response is 3.95. |
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| m6793 | A random sample of 16 junior managers in the offices of corporations in a large city center was taken to estimate average daily commuting time for all such managers. Suppose that the population times have a normal distribution with a mean of 87 minutes and a standard deviation of 22 minutes.
a. What is the standard error of the sample mean commuting time?
b. What is the probability that the sample mean is fewer than 100 minutes?
c. What is the probability that the sample mean is more than 80 minutes?
d. What is the probability that the sample mean is outside the range 85 to 95 minutes?
e. Suppose that a second (independent) random sample of 50 junior managers is taken. Without doing the calculations, state whether the probabilities in parts (b), (c), and (d) would be higher, lower, or the same for the second sample. Sketch graphs to illustrate your answers. |
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| m6794 | A random sample of 16 tires was tested to estimate the average life of this type of tire under normal driving conditions. The sample mean and sample standard deviation were found to be 47,500 miles and 4,200 miles, respectively.
a. Calculate the margin of error for a 95% confidence interval estimate of the mean lifetime of this type of tire if driven under normal driving conditions.
b. Find the UCL and the LCL of a 90% confidence interval estimate of the mean lifetime of this type of tire if driven under normal driving conditions. |
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| m6795 | A random sample of 170 people was provided with a forecasting problem. Each sample member was given, in two ways, the task of forecasting the next value of a retail sales variable. The previous 20 values were presented both as numbers and as points on a graph. Subjects were asked to predict the next value. The absolute forecasting errors were measured. The sample then consisted of 170 differences in absolute forecast errors (numerical minus graphical). The sample mean of these differences was -2.91, and the sample standard deviation was 11.33. Find and interpret the p-value of a test of the null hypothesis that the population mean difference is 0 against the alternative that it is negative. (The alternative can be viewed as the hypothesis that, in the aggregate, people make better forecasts when they use graphs of past history compared to using numerical values from past history.) |
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| m6796 | A random sample of 172 marketing students was asked to rate, on a scale from 1 (not important) to 5 (extremely important), health benefits as a job characteristic. The sample mean rating was 3.31, and the sample standard deviation was 0.70. Test at the 1% significance level the null hypothesis that the population mean rating is at most 3.0 against the alternative that it is larger than 3.0. |
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| m6797 | A random sample of 174 college students was asked to indicate the number of hours per week that they surf the Internet for either personal information or material for a class assignment. The sample mean response was 6.06 hours and the sample standard deviation was 1.43 hours. Based on these results, a confidence interval extending from 5.96 to 6.16 was calculated for the population mean. Find the confidence level of this interval. |
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| m6798 | A random sample of 202 business faculty members was asked if there should be a required foreign language course for business majors. Of these sample members, 140 felt there was a need for a foreign language course. Test the hypothesis that at least 75% of all business faculty members hold this view. Use α = 0.05. |
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| m6799 | A random sample of 38 statistics students from a large statistics class reveals an r of 2 .24 between their test scores on a statistics exam and the time they spent taking the exam. Test the null hypothesis with t, using the .01 level of significance. |
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| m6800 | A random sample of 40 business majors who had just completed introductory courses in both statistics and accounting was asked to rate each class in terms of level of interest on a scale of 1 (very uninteresting) to 10 (very interesting). The 40 differences in the pairs of ratings were calculated and the absolute differences ranked. The smaller of the rank sums, which was for those finding accounting the more interesting, was 281. Test the null hypothesis that the population of business majors would rate these courses equally against the alternative that the statistics course is viewed as the more interesting. |
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| m6801 | A random sample of 5 weeks showed that a cruise agency received the following number of weekly specials to the Caribbean:
20 73 75 80 82
a. Compute the mean, median, and mode.
b. Which measure of central tendency best describes the data? |
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| m6802 | A random sample of 50 personal property insurance policies showed the following number of claims over the past 2 years.
a. Find the mean number of claims per policy.
b. Find the sample variance and standard deviation. |
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| m6803 | A random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population distribution of amounts spent is normal. |
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| m6804 | A random sample of 50 students was asked what salary the college should be prepared to pay to attract the right individual to coach the football team. An independent random sample of 50 faculty members was asked the same question. The 100 salary figures were then pooled and ranked in order (with rank 1 assigned to the lowest salary). The sum of the ranks for faculty members was 2,024. Test the null hypothesis that there is no difference between the central locations of the distributions of salary proposals of students and faculty members against the alternative that in the aggregate students would propose a higher salary to attract a football coach. |
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| m6805 | A random sample of 50 university admissions officers was asked about expectations in application interviews. Of these sample members, 28 agreed that the interviewer usually expects the interviewee to have volunteer experience doing community projects. Test the null hypothesis that one-half of all interviewers have this expectation against the alternative that the population proportion is larger than one-half. Use α = 0.05. |
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| m6806 | A random sample of 60 professional economists was asked to predict whether next year s inflation rate would be higher than, lower than, or about the same as that in the current year. The results are shown in the following table. Test the null hypothesis that the profession is evenly divided on the question.
Prediction Number
Higher ............ 20
Lower ............ 29
About the same ....... 11 |
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| m6807 | A random sample of 80 owners of videocassette recorders was taken. Each sample member was asked to assess the amounts of time in a month spent watching material he or she had recorded from television broadcasts and watching purchased or rented commercially recorded tapes. The 80 differences in times spent were then calculated and their absolute values ranked. The smaller of the rank sums, for material recorded from television, was 1,502. Discuss the implications of this sample result. |
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