In: Statistics and Probability
Question 1 (1 point)
Airline companies recognize that empty seats represent lost revenues that can never be recovered. To avoid losing revenues, the companies often book more passengers than there are available seats. Then, when a flight experiences fewer no-shows than expected, some passengers are 'bumped' from their flights (are denied boarding). Incentives are provided to encourage passengers to give up their reserved seat voluntarily, but occasionally some passengers are involuntarily bumped from the flight. Obviously, these incidents can reflect poorly on customer satisfaction. Suppose Southwest Airlines would like to estimate the true proportion of involuntarily bumped passengers across all domestic flights in the industry. In a pilot sample of 863 domestic passengers, 259 were involuntarily bumped. What is the estimate of the population proportion and what is the standard error of this estimate?
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Question 2 (1 point)
Approximately 43.73% of all businesses are owned by women. If you take a sample of 180 businesses in Michigan, what is the probability that less than 45.32% of them would be owned by women?
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Question 3 (1 point)
Fill in the blank. In a drive thru performance study, the average service time for McDonald's is 217.32 seconds with a standard deviation of 8.5 seconds. A random sample of 62 times is taken. There is a 26% chance that the average drive-thru service time is greater than ________ seconds.
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Question 4 (1 point)
Experimenters injected a growth hormone gene into thousands of carp eggs. Of the 289 carp that grew from these eggs, 23 incorporated the gene into their DNA (Science News, May 20, 1989). With a confidence of 90%, what is the margin of error for the proportion of all carp that would incorporate the gene into their DNA?
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Question 5 (1 point)
You are interested in getting an investment portfolio started with any extra money you make from your part time job while also going to school. While flipping through the latest edition of Money magazine, you read an article that of a survey of magazine subscribers, 179 were randomly selected and analyzed. A 99% confidence interval was constructed for the proportion of all subscribers who made money in the previous year in their investments, which was ( 0.7216 , 0.8762 ). What is the correct interpretation of this confidence interval?
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1.
Estimate of the population proportion = 259 / 863 = 0.3
Standard error = = 0.0156
2) |
Estimate of proportion: 0.3, Standard error: 0.0156. |
2.
p = 0.4373
Standard error = = 0.037
P(p < 0.4532) = P[Z < (0.4532 - 0.4373) / 0.037]
= P[Z < 0.43]
= 0.6664
1) |
0.6664 |
3.
Standard error of mean = 8.5 / = 1.0795
z value for 100 - 26 = 74% percentile is 0.6433
The average drive-thru service time is greater than 217.32 + 0.6433 * 1.0795 = 218.01
4) |
218.01 |
4.
p = 23 / 289 = 0.0796
Standard error = = 0.0159
z value for 90% confidence interval is 1.645
Margin of error = z * Std error = 1.645 * 0.0159 = 0.0261
1) |
0.0261 |
5.
Confidence interval is constructed to make inference for the entire population. Thus, the answer is,
5) |
We are 99% confident that the proportion of all Money magazine subscribers that made money in the previous year from their investments is between 0.7216 and 0.8762. |