| № |
Condition |
free/or 0.5$ |
| m6808 | A random sample of 802 supermarket shoppers determined that 378 shoppers preferred generic-brand items. Test at the 10% level the null hypothesis that at least one-half of all shoppers preferred genericbrand items against the alternative that the population proportion is less than one-half. Find the power of a 10%-level test if, in fact, 45% of the supermarket shoppers preferred generic brands. |
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| m6809 | A random sample of 93 freshmen at the University of Illinois was asked to rate, on a scale of 1 (low) to 10 (high), their overall opinion of residence hall life. They were also asked to rate their levels of satisfaction with roommates, with the floor, with the hall, and with the resident advisor. (Information on satisfaction with the room itself was obtained, but this was later discarded as it provided no useful additional power in explaining overall opinion.) The following model was estimated:
Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε
where
Y = overall opinion of residence hall
X1 = satisfaction with roommates
X2 = satisfaction with floor
X3 = satisfaction with hall
X4 = satisfaction with resident advisor
Use the accompanying portion of the computer output from the estimated regression to write a report summarizing the findings of this study.
Dependent Variable: Y Overall Opinion |
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| m6810 | A random sample of companies was surveyed and asked to indicate if they had used an Internet career service site to search for prospective employees. The companies were also asked questions concerning the posting fee for use of such a site. Is there a relationship between use of such a site and management s opinion on the posting fee? |
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| m6811 | A random sample of customers was asked to select their favorite soft drink from a list of five brands. The results showed that 30 preferred Brand A, 50 preferred Brand B, 46 preferred Brand C, 100 preferred Brand D, and 14 preferred Brand E.
a. Construct a pie chart.
b. Construct a bar chart. |
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| m6812 | A random sample of data for 7 days of operation produced the following (price, quantity) data values:
Price per Gallon of Paint, X Quantity Sold, Y
10 ................. 100
8 ................... 120
5 ................... 200
4 ................... 200
10 ................. 90
7 ................... 110
6 ................... 150
a. Prepare a scatter plot of the data.
b. Compute and interpret b1.
c. Compute and interpret b0.
d. How many gallons of paint would you expect to sell if the price is $7 per gallon? |
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| m6813 | A random sample of data has a mean of 75 and a variance of 25.
a. Use Chebyshev s theorem to determine the percent of observations between 65 and 85.
b. If the data are mounded, use the empirical rule to find the approximate percent of observations between 65 and 85. |
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| m6814 | A random sample of eight homes in a particular suburb had the following selling prices (in thousands of dollars):
192 183 312 227 309 396 402 390
a. Check for evidence of nonnormality.
b. Find a point estimate of the population mean that is unbiased and efficient.
c. Use an unbiased estimation procedure to find a point estimate of the variance of the sample mean.
d. Use an unbiased estimator to estimate the proportion of homes in this suburb selling for less than $250,000. |
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| m6815 | A random sample of Florida tourists was asked a series of questions. Identify the type of data for each question.
a. What is your favorite tourist destination in Florida?
b. How many days do you expect to be in Florida?
c. Do you have children under the age of 10 traveling with you on this visit to Florida?
d. Rank the following Florida attractions in order with 1: most favorite to 5: least favorite. Aquatica Busch Gardens Disney World Kennedy Space Center SeaWorld |
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| m6816 | A random sample of n = 25 is obtained from a population with variance σ2, and the sample mean is computed to be x-bar = 70. Consider the null hypothesis H0: μ = 80 versus the alternative hypothesis H1: μ < 80. Compute the p-value for the following options.
a. The population variance is σ2 = 225.
b. The population variance is σ2 = 900.
c. The population variance is σ2 = 400.
d. The population variance is σ2 = 600. |
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| m6817 | A random sample of n = 25 is obtained from a population with variance σ2, and the sample mean is computed. Test the null hypothesis H0: μ = 100 versus the alternative hypothesis H1: μ > 100 with α = 0.05. Compute the critical value x-barc and state your decision rule for the following options.
a. The population variance is σ2 = 225.
b. The population variance is σ2 = 900.
c. The population variance is σ2 = 400.
d. The population variance is σ2 = 600. |
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| m6818 | A random sample of people from three different job classifications labeled A, B, and C was asked to indicate preferences for three brands of camping lanterns:
Big Star, Lone Star, and Bright Star. The preferences were as follows:
Do these data indicate that there is a difference in ratings for the three different groups? |
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| m6819 | A random sample of six salespeople who attended a motivational course on sales techniques was monitored 3 months before and 3 months after the course. The table shows the values of sales (in thousands of dollars) generated by these six salespeople in the two periods. Assume that the population distributions are normal. Find an 80% confidence interval for the difference between the two population means. |
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| m6820 | A random sample of size n = 16 is obtained from a normally distributed population with a population mean of μ = 100 and a variance of σ2 = 25.
a. What is the probability that x-bar > 101?
b. What is the probability that the sample variance is greater than 45?
c. What is the probability that the sample variance is greater than 60? |
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| m6821 | A random sample of size n = 18 is obtained from a normally distributed population with a population mean of μ = 46 and a variance of σ2 = 50.
a. What is the probability that the sample mean is greater than 50?
b. What is the value of the sample variance such that 5% of the sample variances would be less than this value?
c. What is the value of the sample variance such that 5% of the sample variances would be greater than this value? |
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| m6822 | A random sample of size n = 25 is obtained from a normally distributed population with a population mean of μ = 198 and a variance of σ2 = 100.
a. What is the probability that the sample mean is greater than 200?
b. What is the value of the sample variance such that 5% of the sample variances would be less than this value?
c. What is the value of the sample variance such that 5% of the sample variances would be greater than this value? |
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| m6823 | A random sample of statistics professors was asked to complete a survey including questions on curriculum content, computer integration, and software preferences. Of the 250 responses, 100 professors indicated that they preferred software package M and 80 preferred software package E, whereas the remainder were evenly split between preference for software package S and software package P. Do the data indicate that professors have a preference for any of these software packages? |
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| m6824 | A random sample of women is obtained, and each person in the sample is asked if she would purchase a new shoe model. The new shoe model would be successful in meeting corporate profit objective if more than 25% of the women in the population would purchase this shoe model. The following hypothesis test can be performed at a level of α = 0.03 using p` as the sample proportion of women who said yes.
H0: P ≤ 0.25
H1: P > 0.25
What value of the sample proportion, p`, is required to reject the null hypothesis, given the following sample sizes?
a. n = 400
b. n = 225
c. n = 625
d. n = 900 |
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| m6825 | A random sample tends not to be an exact replica of its parent population. This fact has a number of implications. Indicate which are true and which are false.
(a) All possible random samples can include a few samples that are exact replicas of the population, but most samples aren’t exact replicas.
(b) A more representative sample can be obtained by handpicking (rather than randomly selecting) observations.
(c) Insofar as it misrepresents the parent population, a random sample can cause an erroneous generalization.
(d) In practice, the mean of a single random sample is evaluated relative to the variability of means for all possible random samples. |
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| m6826 | A random variable X is normally distributed with a mean of 100 and a variance of 100 and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to 0.5. Find the mean and variance of the random variable:
W = 5X + 4Y |
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| m6827 | A random variable X is normally distributed with a mean of 100 and a variance of 100, and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to -0.5. Find the mean and variance of the random variable:
W = 5X + 4Y |
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