Answered: (10 points) We want to estimate the… | bartleby

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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1. (10 points) We want to estimate the proportion of vaping products containing dangerous
additives like Vitamin E acetate in vaping products. The CDC took a sample of 37 vaping
products and found that 17 contained Vitamin E acetate.
a) Construct a 90% confidence interval for the proportion of all vaping products that
contain Vitamin E acetate. Round to three decimal places.
b) Interpret the interval you found above.

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A sociologist is comparing the proportion of teenage boys who receive a text message at least once an hour to the percentage of teenage girls who do. She has collected data from 150 men and 150 women. Which of the following is not a condition that the sociologist should check before creating a confidence interval for the difference in population proportions?
It is being desired to estimate the average daily emission, in tons, of sulfur oxides by a large industrial plant. If n=40, 19.6 tons and s=5.51 tons. Construct a 95 percent large-sample confidence interval for the plant’s true average daily emission of sulfur oxides.
1) A consumer magazine polls cell-phone-users to see if they are happy with their phones and would purchase the same model again. They randomly selected cell-phone-users and found the following: 429 of 550 owners of iPhones would purchase their phone again, and 324 of 450 owners of Androids would purchase the same phone again. a) Check the assumptions for comparing proportions . b) Find a 95% confidence interval (Two-Proportion z-Interval) for the difference in the proportions. c) Interpret your interval in the context of the problem. What does the confidence interval say about the difference in the satisfaction of the two types of owners? Hint: pay attention to the signs on the LB & UB .
Suppose that, for budget planning purposes, the city in the previous exercise needs a better estimate of the mean daily income from parking fees. a) Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. How would this interval be better for the city? (You need not actually create the new interval.) b) How would the 95% interval be worse for the planners? c) How could they achieve an interval estimate that would better serve their planning needs?
It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users who have liver damage. For participating in this study, he will pay each subject $20 and provide a free medical consultation if the patient has liver damage. a) If he wants to limit the margin of error of his 95% confidence interval to 1%, what is the minimum amount of money he needs to set aside to pay his subjects?
2. The Vice-Chancellor of a university is concerned that illicit drug use on campus is higher than the 5% acceptable level. A random sample of 140 students revealed that 5 of them had used illicit drug during the last 12 months. Construct a 90% confidence interval to estimate the true proportion of students who use illicit drug. Should the Vice-Chancellor be concerned?
In one of the studies, it was found that, in a random sample of 261 married persons, 135 were smokers while in a sample of 239 non-married persons there were 131 smokers. a) Find a 90% confidence interval for the true difference in proportion of smokers among the married and non-married populations. Interpret this confidence interval. b) Based on the above interval, can one conclude that there is a significant difference between the proportions of smokers in the two populations ? Justify your answer. c) Do a formal hypothesis testing to test whether the two populations’ proportions are significantly different. Use α = 0.10 and a p−value method. Set up the appropriate null and alternative hypotheses. Is the conclusion same as the one in part(b)?

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