# 1. According to a recent poll, 26% of adults in a certain area hav...

## Transcribed Text

1. According to a recent poll, 26% of adults in a certain area have high levels of cholesterol. They report that such elevated levels "could be financially devastating to the regions healthcare system" and are a major concern to health insurance providers. According to recent studies, cholesterol levels in healthy adults from the area average about 210 mg/dL, with a standard deviation of about 35 mg/dL. and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy adults from the region is taken, answer parts (a) through (d). (a) What shape will the sampling distribution of the mean have? A. The sampling distribution of the mean is normal. 8. The sampling distribution of the mean is skewed right. C. The sampling distribution of the mean is skewed left. D. There is not enough information to determine the shape of the sampling distribution (b) What is the mcan of the sampling distribution? um mg/dL (c) What is the standard deviation? SD(y) - mg/dL (Round to two decimal places as needed.) (d) If the sample size were increased to 120. how would your answers to parts (a)-(c) change? also be normally distributed. For part (a). the shape of the distribution would become skewed left. become skewed right. For part (b), the mean of the sampling distribution would change to n- mg/dL. remain as 1. (cont.) For part (c). the standard deviation of the sampling distribution would change to SD(y)= remain as mg/dL. (Round to two decimal places as needed.) 2. A marketing researcher for a phone company surveys 150 people and finds that the proportion of clients who are likely to switch providers when their contract expires is 0.14. Use this information to complete parts (a) and (b). (a) What is the standard deviation of the sampling distribution of the proportion? SE(p) - (Round to four decimal places as needed.) (b) If the rescarcher wants to reduce the standard deviation by half. how large a sample would the researcher need? (Type a whole number.) 3. A survey of 25 randomly selected customers found the ages shown 24 49 29 39 (in years). The mean is 32.84 years and the standard deviation is 39 20 19 43 19 8.88 years. a) What is the standard error of the mean? 35 40 36 33 23 b) How would the standard crror change if the sample size had been 23 38 33 34 42 400 instead of 25? (Assume that the sample standard deviation didn't 40 29 46 38 30 change.) a) The standard error of the mean is . (Round to two decimal places as needed.) b) How would the standard crror change if the sample size was 400 instead of 25 with the same sample standard deviation? Select the correct choice below and fill in any answer boxes within your choice. A. The standard crror would increase. The new standard crror would be times the old. B. The standard crror would decrease. The new standard error would be the old standard error divided by . C. The standard error would not change. 4. For parts a and b, use the t tables, software, or a calculator to estimate. a) the critical value of t for a 90% confidence interval with df= 22. b) the critical value oft for a 95% confidence interval with df=78. a) What is the critical value of t for a 90% confidence interval with df= 22? (Round to two decimal places as needed.) b) What is the critical value of t for a 95% confidence interval with df= 78? (Round to two decimal places as needed.) 5. The histogram shows the ages (in years) of 25 customers that were in the freezer aisle at a large grocery store. Check the 10- assumptions and conditions for an inference using Student's 8- t-model 6 4- 2- 0- 15 30 45 Which assumptions and conditions are satisfied by the sample? The Independence Assumption is satisfied. is not The Randomization Condition is not satisfied. is The 10% Condition is not satisfied is The Nearly Normal Condition is not satisfied. is 6. An analyst collected data from 25 randomly selected 21.34 46.91 18.22 18.37 19.34 transactions and found the purchase amounts (in \$). The 5.78 27.24 30.78 19.02 18.18 mean is \$22.03 and the standard deviation is \$13.07. The 7.39 21.61 32.36 23.86 46.78 analyst wants to know if the mean purchase amount of all transactions is at least \$15. Use the given information to 3.24 10.57 43.42 18.98 4.49 complete parts a through c. 31.42 3.33 41.44 15.58 21.21 a) What is the null hypothesis? Ho: \$ - y " (Type an integer or a decimal.) b) Is the alternative one- or two-sided? The alternative hypothesis is one-sided. two-sided. c) What is the value of the test statistic? The test statistic is . (Round to two decimal places as needed.) d) What is the P-value of the test statistic? P-value - (Round to four decimal places as needed.) e) What do you conclude at a - 0.005? The P-value is less than a,so fail to reject the null hypothesis. There is sufficient greater than reject insufficient evidence to conclude that the mean purchase amount of all transactions is greater than \$15. 7. Describe how the width of a 95% confidence interval for a mean changes as the standard deviation (s) of a sample increases, assuming sample size remains the same. Choose the correct answer below. DA As the variability of a sample increases, the width of a 95% confidence interval decreases, assuming that sample size remains the same. B. As the variability of a sample increases, the width of a 95% confidence interval increases, assuming that sample size remains the same. OC. As the variability of a sample increases, the width of a 95% confidence interval remains the same, assuming that sample size remains the same. 8. Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. For a random sample of 44 weekdays, daily fees collected averaged \$126, with a standard deviation of \$15. Suppose that for budget planning purposes. the city needs a better estimate of the mean daily income from parking fees. Complete parts (a) through (c). (a) Somcone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval the city first created. Would this increased interval be better for the city? (You need not actually create the interval.) A. Yes. A 95% confidence level gives increased confidence that the mean parking revenue is contained with the interval. B. Yes. A 95% confidence level means that more people were sampled so the interval is more accurate. C. No. There is no significant difference between using the 90% confidence level and the 95% confident level. (b) Would the 95% confidence interval be worse for the planners? A. Yes. A 95% confidence level creates a narrower interval and is, therefore. more precisc and will cost the planners more moncy. B. Yes. The increased confidence level creates a wider interval and is. therefore. less precisc. C. No. The increased confidence interval would not be worse for the planners. (c) How could they achieve a confidence interval estimate that would better serve their planning needs? A. They could include the weekend parking fees in the sample. 3. They could collect a larger sample which would create a more precise interval without sacrificing confidence. C. The city officials and planner could compromise and use a 92.5% confidence interval. 9. A certain region has been one of the fastest growing regions for a number of years. Accompanying the rapid growth are massive new construction projects that create visible dust pollution. As required by government regulation, researchers continually monitor pollution levels. In the most recent test of pollution levels, 121 air samples were collected. The dust particulate levels must be reported to the federal regulatory agencies. In the report sent to the federal agency, it was noted that the mean particulate level is 57.6 micrograms/cubic liter of air, and the 95% confidence interval estimate is (52.06 mg to 63.07 mg). A graph of the distribution of the particulate amounts was also included and is shown below. Complete parts a and b. Click the icon to view the histogram of the particulate amounts. a) Of the following choices, what are the assumptions and conditions we typically make when preparing to use Student's t inference methods. Select all that apply. A. The data arise from a random sample or suitably randomized experiment. B. The data come from a nearly Normal distribution. C. The sample size is at least 10. D. The expected values for the numbers of successes and failures are at least 10. b) Do you think the confidence interval noted in the report is valid? Briefly explain why or why not. Choose the correct answer below. A. Yes: although the data produce a histogram that is not incarly Normal, the sample size is large enough. B. No; the expected values for the numbers of successes and failures are less than 10. DC. Yes: the sample is random, the histogram is nearly Normal, and the sample size is greater than 10. Do. No: the data do not appear to come from a nearly Normal distribution. 9. 20 (cont.) 15- 10- 5- o 20 40 60 80 100 Particulates (in mictograms per cubic liter of ait) 10. A market researcher at a major clothing company that has traditionally relied on catalog mail-order sales decides to investigate whether the amount of monthly online sales has changed. She compares the mean monthly online sales of the past several months with a historical figure for mean monthly sales for online purchases. She gets a P-value of 0.01. Explain in this context what the 1% means. What does the 1% P-value mean? A. Online purchases make up 1% of all sales. Because the percentage of online sales is so small, the resulting mean is insignificant. B. Online purchases make up 1% of all sales. The resulting mean sales would not occur assuming the historical mean for sales. C. If the mean monthly sales due to online purchases has not changed. there is a 1% chance (or I out of every 100 samples) that the resulting mean sales would occur assuming the historical mean for sales. D. If the mean monthly sales due to online purchases has changed, there is a 1% chance (or I out of every 100 samples) that the resulting mean sales would not occur assuming the historical mcan for sales.

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1 a. Choice A
b. 210 mg/dL
c. 5.40 mg/dL
d. also be normally distributed
210 mg/dL
3.20...

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