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free/or 0.5$ |
| m6848 | A researcher intends to estimate the effect of a drug on the scores of human subjects performing a task of psychomotor coordination. The members of a random sample of 9 subjects were given the drug prior to testing.
The mean score in this group was 9.78, and the sample variance was 17.64. An independent random sample of 10 subjects was used as a control group and given a placebo prior to testing. The mean score in this control group was 15.10, and the sample variance was 27.01. Assuming that the population distributions are normal with equal variances, find a 90% confidence interval for the difference between the population mean scores. |
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| m6849 | A researcher randomly assigns college freshmen to either of two experimental conditions. Because both groups consist of college freshmen, someone claims that it is appropriate to use a t test for the two related samples. Comments? |
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| m6850 | A researcher suspected that the number of between meal snacks eaten by students in a day during final examinations might depend on the number of tests a student had to take on that day. The accompanying table shows joint probabilities, estimated from a survey.
a. Find the probability distribution of X and compute the mean number of tests taken by students on that day.
b. Find the probability distribution of Y and, hence, the mean number of snacks eaten by students on that day.
c. Find and interpret the conditional probability distribution of Y, given that X = 3.
d. Find the covariance between X and Y.
e. Are number of snacks and number of tests independent of each other? |
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| m6851 | A restaurant manager classifies customers as regular, occasional, or new, and finds that of all customers 50%, 40%, and 10%, respectively, fall into these categories. The manager found that wine was ordered by 70% of the regular customers, by 50% of the occasional customers, and by 30% of the new customers.
a. What is the probability that a randomly chosen customer orders wine?
b. If wine is ordered, what is the probability that the person ordering is a regular customer?
c. If wine is ordered, what is the probability that the person ordering is an occasional customer? |
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| m6852 | A restaurant manager receives occasional complaints about the quality of both the food and the service. The marginal probability distributions for the number of weekly complaints in each category are shown in the accompanying table. If complaints about food and service are independent of each other, find the joint probability distribution. |
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| m6853 | A robbery has been committed and McGuff, the crime-fighting dog, has been called in to investigate. He discovers that Sally Coldhands was seen wearing gloves in the neighborhood shortly after the crime, and, thus, he concludes that she should be arrested. From past experience you know that 50% of the people that McGuff says should be arrested for robbery are actually guilty. Before making the arrest, you order some additional investigation. From a large population of convicted robbers, you find that 60% wore gloves at the time of the crime and continued to wear them for an interval after the crime. Further investigation reveals that 80% of the people in the neighborhood of the crime were wearing gloves around the time of the crime.
a. Based on the fact that Sally was wearing gloves, what is the probability that Sally actually committed the crime?
b. If you charged her with the crime, do you think a jury would convict her based on the glove evidence? Explain why or why not. |
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| m6854 | A salesperson receives an annual salary of $6,000 plus 8% of the value of the orders she takes. The annual value of these orders can be represented by a random variable with a mean of $600,000 and a standard deviation of $180,000. Find the mean and standard deviation of the salesperson s annual income. |
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| m6855 | A sample of 100 students is to be taken to determine which of two brands of beer is preferred in a blind taste test. Suppose that, in the whole population of students, 50% would prefer brand A.
a. What is the probability that more than 60% of the sample members prefer brand A?
b. What is the probability that between 45% and 55% of the sample members prefer brand A? |
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| m6856 | A sample of 11 managers in retail stores having selfcheckout was asked if customers have a positive attitude about the scanning process. Seven managers answered yes, and four answered no. Test against a two-sided alternative the null hypothesis that, for the population of managers, responses would be equally divided between yes and no. |
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| m6857 | A sample of 12 senior executives found the following results for percentage of total compensation derived from bonus payments:
15.8 17.3 28.4 18.2 15.0 24.7 13.1 10.2 29.3 34.7 16.9 25.3
a. Compute the sample median.
b. Compute the sample mean. |
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| m6858 | A sample of 20 financial analysts was asked to provide forecasts of earnings per share of a corporation for next year. The results are summarized in the following table:
a. Construct the histogram.
b. Determine the relative frequencies.
c. Determine the cumulative frequencies.
d. Determine and interpret the relative cumulative frequencies. |
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| m6859 | A sample of 20 financial analysts was asked to provide forecasts of earnings per share of a corporation for next year. The results are summarized in the following table:
Forecast ($ per share) Number of Analysts
$9.95 to under $10.45 .......... 2
$10.45 to under $10.95 ......... 8
$10.95 to under $11.45 ......... 6
$11.45 to under $11.95 ......... 3
$11.95 to under $12.45 ......... 1
a. Estimate the sample mean forecast.
b. Estimate the sample standard deviation. |
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| m6860 | A sample of 25 blue-collar employees at a production plant was taken. Each employee was asked to assess his or her own job satisfaction (x) on a scale of 1 to 10. In addition, the numbers of days absent (y) from work during the last year were found for these employees. The sample regression
y`i = 11.6 – 1.2x
Line was estimated by least squares for these data. Also found were
a. Test, at the 1% significance level against the appropriate one-sided alternative, the null hypothesis that job satisfaction has no linear effect on absenteeism.
b. A particular employee has job satisfaction level 4. Find a 90% interval for the number of days this employee would be absent from work in a year. |
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| m6861 | A sample of 33 accounting students recorded the number of hours spent studying the course material during the week before the final exam. The data are stored in the data file Study.
a. Compute the sample mean.
b. Compute the sample median.
c. Comment on symmetry or skewness.
d. Find the five-number summary for this data. |
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| m6862 | A sample of 33 accounting students recorded the number of hours that they spent studying for a final exam. The data are stored in the data file Study.
a. Give an example of an unbiased, consistent, and efficient estimator of the population mean.
b. Find the sampling error for a 95% confidence interval estimate of the mean number of hours students studied for this exam. |
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| m6863 | A sample of 75 corporations buying back franchises was examined. Of these cases, returns on common stock around the buyback announcement date were positive 52 times, negative 15 times, and zero 8 times.
Test the null hypothesis that positive and negative returns are equally likely against the alternative that positive returns are more likely. |
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| m6864 | A school psychologist wishes to determine whether a new antismoking film actually reduces the daily consumption of cigarettes by teenage smokers. The mean daily cigarette consumption is calculated for each of eight teen-age smokers during the month before and the month after the film presentation, with the following results:
When deciding on the form of the alternative hypothesis, H1, remember that a positive difference score (D = X1 – X2) reflects a decline in cigarette consumption.)
(a) Using t, test the null hypothesis at the .05 level of significance.
(b) Specify the p - value for this test result.
(c) If appropriate (because the null hypothesis was rejected), construct a 95 percent confidence interval for the true population mean for all difference scores, and use Cohen’s d to obtain a standardized estimate of the effect size. Interpret these results.
(d) What might be done to improve the design of this experiment? |
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| m6865 | A screening procedure was designed to measure attitudes toward minorities as managers. High scores indicate negative attitudes and low scores indicate positive attitudes. Independent random samples were taken of 151 male financial analysts and 108 female financial analysts. For the former group the sample mean and standard deviation scores were 85.8 and 19.13, whereas the corresponding statistics for the latter group were 71.5 and 12.2. Test the null hypothesis that the two population means are equal against the alternative that the true mean score is higher for male than for female financial analysts. |
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| m6866 | A securities analyst claims that, given a specific list of 6 common stocks, it is possible to predict, in the correct order, the 3 that will perform best during the coming year. What is the probability of making the correct selection by chance? |
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| m6867 | A senior manager, responsible for a group of 120 junior executives, is interested in the total amount of time per week spent by these people in internal meetings.
A random sample of 35 of these executives was asked to keep diary records during the next week. When the results were analyzed, it was found that these sample members spent a total of 143 hours in internal meetings.
The sample standard deviation was 3.1 hours.
Find a 90% confidence interval for the total number of hours spent in internal meetings by all 120 junior executives in the week. |
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