1. A public opinion poll on the 2016 presidential race was conducted by surveying 1,000 randomly...

1. A public opinion poll on the 2016 presidential race was conducted by surveying 1,000 randomly selected registered voters. It was found that 59% of all registered voters intended to vote Democrat. To determine whether this is representative of your town, you conduct a survey of a random sample of 75 voters in your town.

Calculate the mean of the sampling distribution of the national sample proportion.

2. The marketing team at Caya Shoe Company has determined their top running shoe has a probability of 0.59 to be chosen over a competing brand by female consumers. This was determined by field-testing the shoe with a similar shoe from a competing brand. One hundred women were asked to try both pairs of shoes and choose one pair to keep as payment for their participation. To avoid bias, the women had no way of knowing whether Caya Shoes or the competing brand was conducting the survey. The marketing director selects a random sample of 17 customers to determine whether this is the true probability.

Calculate the standard deviation of the sampling distribution of the sample proportion. (Round your answer to three decimal places.)

3. Consider a small population consisting of the 100 students enrolled in an introductory statistics course. Students in the class completed a survey on academic procrastination. The average number of hours spent procrastinating when they should be studying, per exam, by all students in this course is 5 hours with a standard deviation of 3 hours. The distribution of amount of time students spend procrastinating is known to be normal.

(a) Identify the value (in hours) of the population mean.

(b) Calculate the standard deviation (in hours) of the sampling distribution of the sample mean for a sample of size 18 drawn from this population. (Round your answer to three decimal places.)

(c) What is the probability of obtaining a sample mean of less than 2 hours based on a sample of size 18 if the population mean truly is 5 hours? (Use a table or technology. Round your answer to five decimal places.)

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orchestra answered 1 year ago

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