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You would like to construct a 99% confidence interval to estimate the population mean price of milk (per gallon) in your city. You select a random sample of prices from different stores. The sample has a mean of 3.49 dollars and a standard deviation of 0.28 dollars.(a) What is the best point estimate, based on the sample, to use for the population mean?dollars(b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 99% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)Sampling scenario Z t Could use either Z or t UnclearThe sample has size 19, and it is from a normally distributed population with a known standard deviation of 0.31. Zt The sample has size 14, and it is from a normally distributed population with an unknown standard deviation. Zt The sample has size 80, and it is from a non-normally distributed population. Zt CheckSave For LaterSubmit Assignment

Question

You would like to construct a 99% confidence interval to estimate the population mean price of milk (per gallon) in your city. You select a random sample of prices from different stores. The sample has a mean of 3.49 dollars and a standard deviation of 0.28 dollars.(a) What is the best point estimate, based on the sample, to use for the population mean?dollars(b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 99% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)Sampling scenario Z t Could use either Z or t UnclearThe sample has size 19, and it is from a normally distributed population with a known standard deviation of 0.31. Zt The sample has size 14, and it is from a normally distributed population with an unknown standard deviation. Zt The sample has size 80, and it is from a non-normally distributed population. Zt CheckSave For LaterSubmit Assignment

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Solution

(a) The best point estimate for the population mean, based on the sample, is the sample mean itself. So, the best point estimate is $3.49.

(b) For the sampling scenarios:

  1. The sample has size 19, and it is from a normally distributed population with a known standard deviation of 0.31.

    • In this case, we should use the Z distribution. This is because the population standard deviation is known and the sample size is less than 30.
  2. The sample has size 14, and it is from a normally distributed population with an unknown standard deviation.

    • In this case, we should use the t distribution. This is because the population standard deviation is unknown and the sample size is less than 30.
  3. The sample has size 80, and it is from a non-normally distributed population.

    • In this case, we should use the Z distribution. This is because the sample size is large (greater than 30), and according to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normally distributed regardless of the shape of the population distribution.

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