1.) In order to increase revenue, many video game publishers sell downloadable c
ID: 3199441 • Letter: 1
Question
1.) In order to increase revenue, many video game publishers sell downloadable content (DLC) separately from the main game. Such content could include additional costumes for the playable characters, additional online game modes, special weapons, etc. A recent industry survey polled 936 game players ages 20 to 30 asking them how important DLC was to their enjoyment of a game. In that sample, 552 people reported that DLC was "very important" to them. Suppose that the company conducting the survey wants to test the hypothesis that the true population proportion of game players who believe DLC is "very important" is 0.5. Calculate the value of the test statistic to two decimal places.
2.) A researcher wants to estimate the true proportion of people who would buy items they know are slightly defective from thrift shops because of the lower price. After conducting a survey on a sample of 827 persons who regularly shop at thrift stores, he finds that 258 of the individuals would buy a slightly defective item if it cost less than a dollar. Calculate the lower bound of a 90% confidence interval for the true proportion of people who would purchase a defective item. Take all calculations to three (3) decimal places.
3.) A researcher wishes to test the hypothesis that the mean age at first marriage for women in Texas is less than 23.7. In a sample of 31 Texas women, he finds that the average age is 23.4 with a standard deviation of 5.8. Calculate the test statistic to two decimal places.
4.) A researcher wants to study sports-watching behavior of young men. In a random sample of 30 young adult men 20-30 years old, each person was asked how many minutes of sports he watched on TV daily. The researcher wishes to test whether the mean amount of television watched daily by young men is greater than 49 minutes. Suppose the sample mean is 59.4 and the sample standard deviation is 8.4. Calculate the test statistic to two decimal places.
5.) Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here is the data: 27.64, 11.54, 28.7, 10.19, 18.36, 27.47, 17.42, 24.37. He wishes to test the null hypothesis that the average amount of money people have in their pockets is equal to $20. Calculate the test statistic to two decimal places. Take all calculations toward the answer to three decimal places.
6.) A marketing manager needs to estimate the true mean dollar amount spent by members of Amazon Prime to determine if targeted advertising efforts for the service at the point of checkout should be adjusted to reflect a difference in mean spending from previous amounts. She obtains the following sample statistics from a sample of 100 Amazon Prime members who recently made a purchase: n 100 top enclose y 1400 s 250 Using this information, she she can be 98% confident that the true mean amount spent is between $ and $ . Enter your answers to the nearest whole dollar amount.
Explanation / Answer
1)
Formulating the null and alternatuve hypotheses,
Ho: p = 0.5
Ha: p =/= 0.5
As we see, the hypothesized po = 0.5
Getting the point estimate of p, p^,
p^ = x / n = 0.835805085
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.016273614
Getting the z statistic,
z = (p^ - po) / sp = 20.63494239
z = 20.63
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