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Chapter 8: Q 41. (page 522)

Video games A Pew Research Center report on gamers and gaming

estimated that 49% of U.S. adults play video games on a computer, TV, game console, or portable device such as a cell phone. This estimate was based on a random sample of 2001 U.S. adults. Construct and interpret a 95% confidence interval for the proportion of all U.S. adults who play video games.

Short Answer

Expert verified

The confidence interval is(0.468,0.512)

Step by step solution

01

Given Information

It is given that p^=49%=0.49

n=2001

02

Concept Used

Formula to be used isCI=p^±za/2×p^(1-p^)n

03

Calculation

From normal standard table, at 95%confidence interval, zscore is 1.96

95%confidence interval is calculated as

CI=p^±zα/2×p^(1-p^)n

=0.49±1.96×0.49(1-0.49)2001

(0.468,0.512)

Hence, probability is 95%that proportion of adults playing video games lies in range(0.468,0.512)

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Most popular questions from this chapter

In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we not be safe constructing the interval based on an SRS of size14from the population?

a. A stemplot of the data is roughly bell-shaped.

b. A histogram of the data shows slight skewness.

c. A boxplot shows that the values above the median are much more variable than the values below the median.

d. The sample standard deviation is large.

e. The sample standard deviation is small.

Price cuts (4.2) Stores advertise price reductions to attract customers. What type of price
cut is most attractive? Experiments with more than one factor allow insight into
interactions between the factors. A study of the attractiveness of advertised price discounts
had two factors: percent of all foods on sale (25%, 50%, 75%, or 100%) and whether the discount was stated precisely (e.g., as in “60% off”) or as a range (as in “40% to 70% off”). Subjects rated the attractiveness of the sale on a scale of 1 to 7.
a. List the treatments for this experiment, assuming researchers will use all combinations of the two factors.
b. Describe how you would randomly assign 200 volunteer subjects to treatments.
c. Explain the purpose of the random assignment in part (b).
d. The figure shows the mean ratings for the eight treatments formed from the two factors.35 Based on these results, write a careful description of how percent on sale and precise discount versus range of discounts influence the attractiveness of a sale.

Going to the prom Tonya wants to estimate the proportion of seniors in her school who plan to attend the prom. She interviews an SRS of 20of the 750seniors in her school and finds that 36plan to go to the prom.

Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172172undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” Only 19answered “Yes.” Assume the conditions for inference are met.

a. Determine the critical valueZ*for a 96%confidence interval for a proportion.

b. Construct a 96%confidence interval for the proportion of all undergraduates at this university who would go to the professor.

c. Interpret the interval from part (b).

Losing weight Refer to Exercise 6.

a. Explain what would happen to the length of the interval if the confidence level was decreased to 90%.

b. How would a 95%confidence interval based on triple the sample size compare to the original 95%interval?

c. As Gallup indicates, the 3percentage point margin of error for this poll includes only sampling variability (what they call “sampling error”). What other potential sources of error (Gallup calls these “non sampling errors”) could affect the accuracy of the 95% confidence interval?
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