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62% of Amazon customers have a Prime account. For a market research study, Amazon selects 500 customers at random from their customer database and tests whether or not they have a Prime account. What is the standard error of the sampling distribution for the proportion of customers with a Prime account? Round your answer to at least three decimal places.

Does your answer to 13d make sense, given the confidence interval calculated in 13a-b?  Why?

Does your answer to 13d make sense, given the confidence interval calculated in 13a-b?  Why?

Does your answer to 13d make sense, given the confidence interval calculated in 13a-b?  Why?

A pet food company claims their canned food contains 2.5oz of real chicken. Suppose we take a random sample of 250 cans of cat food from Walmart’s around the area to perform a hypothesis test and find a p-value of .02.  If we use the same sample to produce a 95% confidence interval, what would be true?

Suppose a survey of 912 cars listed for sale in Florida in 2020 finds an average price of $13,800 with a standard deviation of $3,140. Suppose the average price of a car for sale in Florida in 2019 was $12,900.  Perform a hypothesis test to see whether the average price is any different in 2020 (could be greater or less): set up a null and alternate hypothesis, find a p-value, and conclude whether to reject the null hypothesis. What is the p-value?  Round your answer to at least three decimal places.

An auto parts manufacturer claims that less than 12% of their batteries will need to be replaced within the first year. A lawsuit challenges that claim, saying that out of 638 reported purchases, 103 of them needed to be replaced within the first year. What would be the null and alternate hypotheses for a statistical test of the company’s claim using the sample taken in the lawsuit?

Suppose a survey of 912 cars listed for sale in Florida in 2020 finds an average price of $13,800 with a standard deviation of $3,140. Suppose the average price of a car for sale in Florida in 2019 was $12,900.  Perform a hypothesis test to see whether the average price is any different in 2020 (could be greater or less): set up a null and alternate hypothesis, find a p-value, and conclude whether to reject the null hypothesis. What is the p-value?  Round your answer to at least three decimal places.

An auto parts manufacturer claims that less than 12% of their batteries will need to be replaced within the first year. A lawsuit challenges that claim, saying that out of 638 reported purchases, 103 of them needed to be replaced within the first year. Perform the hypothesis test for the sample data. What is the p-value? Round your answer to three decimal places.

The average order on Amazon is for $47.31, with a standard deviation of $4.83.  If the average orders are compared for a sample of 500 customers, what is the standard deviation of the sampling distribution? Round your answer to at least two decimal places.