8. A large online retailer is analyzing how frequently their product WonderWidget" is returned. Out of 345 WonderWidgets bought, 48 were returned. (a) Find the 97% confidence interval for the long-run proportion of Wonder Widgets returned. (b) If the retailer wanted to obtain a 97% confidence interval with a margin of error ±0.03, how many purchases it should analyze?
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- Joe’s Pizza Joint found that 64.2% of the 328 pizzas sold last week included pepperoni. Find a98% confidence interval for the proportion of Joe’s customers that order pepperoni.A scientist wondered if there was a difference in the average daily intake of dairy products between men and women. He took a sample of n1 = 50 adult men and n2 = 50 adult women and recorded their daily intakes of dairy products in grams per day. A summary of the sample results of it is presented in the table. He constructs a 95% confidence interval for the difference in the average daily intakes of dairy products for men and women. Can it be concluded that there is a difference in the average daily intakes for men and women?In a random sample of 250 high school students, it was found that 85.2% (213) of them later graduated. The 95% confidence interval is (-0.065,0.065) and the 98% confidence interval is (-0.077,0.077) for the true proportion of all high school students who graduate. Compare the two proportions.
- A new drug to treat high cholesterol is being tested by pharmaceutical company. The cholesterol levels for 8 patients were recorded before administering the drug and after. The mean difference in total cholesterol levels (after - before) was 15.91 mg/dL with a standard deviation of 15.2714 mg/dL. Create a 95% confidence interval for the true average difference in cholesterol levels by the drug. Question 9 options: 1) (-3.1428, 28.6772) 2) (3.1428, 28.6772) 3) (3.4593, 28.3607) 4) (10.5107, 21.3093) 5) (13.5454, 18.2746)A poll reported that only 645 out of a total of 2029 adults in a particular region said they had a "great deal of confidence" or "quite a lot of confidence" in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met. Find a 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools, and interpret this interval. The 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is ____A poll reported that only 507 out of a total of 1809 adults in a particular region said they had a "great deal of confidence" or "quite a lot of confidence" in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met. Find a 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools, and interpret this interval.
- 11Suppose that you're regressing the Sales Price (the y-variable) of a home on the Square Footage (the x-variable) of that home, and the 95% Confidence Interval (CI) estimate of B1 is given by the interval: (-2.757,3031). Give the interpretation of this CI. Specifically, EXPLAIN how the CI answers the question about whether or not Home Prices and Square Footage are, or are not, significantly linearly related.You want to estimate the proportion of park visitors that bring food to the park. If you took an SRS of visitors, and 43 out of 100 visitors brought food with them, find the 95% confidence interval for the proportion of visitors that bring food. The Parks Department found that 48% of visitors to parks brought food to the park back in 2005. Use the results from the first part to see if that proportion has changed. Be sure to include appropriate hypotheses, the p-value, and your conclusions.
- In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago. In a sample of 50 women, 48 women said that they had less leisure time than they had 10 years ago. Find the 90% confidence interval for the difference of the two proportions. (0.372, 0.508) (-0.097,0.297) (-0.168, 0.008) (-0.032,0.192)6. Of 400 randomly selected medical students, 21 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.A statistical study is made to compare the % of smokers in small rural towns to the overall smoking rate of the US. Of 1500 asults selected randomly from small towns it is found that 285 of them smoke. With a cofidence interval of (017, 0.21). The CDC reports that 15.1% of all American adults smoke. Does the confidence interval suggest that smoking rate is higher in small towns than in the country overall?