Question

You would like to construct a 90% confidence interval to estimate today's population mean temperature, so you make a series of measurements (a random sample) throughout the day. The mean of these measurements is 59 degrees Fahrenheit, and their standard deviation is 3.2 degrees Fahrenheit. (a) What is the best point estimate, based on the sample, to use for the population mean? х $ ? I degrees (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 90% confidence interval for the population mean. (In the table, Z refers to a standard normal distribution, and t refers to a t distribution.) A Sampling scenario z t Could use either Zort Unclear х ? The sample has size 15, and it is from a normally distributed population with an unknown standard deviation. O The sample has size 95, and it is from population non-normally distributed O e The sample has size 90, and it is from a non-normally distributed population with a known standard deviation of 3.3. O

Answer 1

The best point estimate for the population mean is the sample mean of 59 degrees Fahrenheit. The t distribution should be used for a sample size of 15 from a normally distributed population with an unknown standard deviation. The z distribution should be used for a sample size of 90 from a non-normally distributed population with a known standard deviation of 3.3.

Step-by-step explanation:

(a) The best point estimate, based on the sample, to use for the population mean is the sample mean itself. In this case, the sample mean is 59 degrees Fahrenheit.

(b) For each of the sampling scenarios:

• The sample has size 15, and it is from a normally distributed population with an unknown standard deviation. In this case, the t distribution should be used to calculate the critical value.
• The sample has size 95, and it is from a population non-normally distributed. In this case, it is unclear which distribution should be used, as the information given is insufficient.
• The sample has size 90, and it is from a non-normally distributed population with a known standard deviation of 3.3. In this case, the z distribution should be used to calculate the critical value.