You would like to construct a 95% 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 4 degrees Fahrenheit. (a) What is the best point estimate, based on the sample, to use for the population mean? O degrees (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 95% confidence interval for the population mean. (In the table, Z refers to a standard normal distribution, and t refers to a t distribution.) Could use

MATLAB: An Introduction with Applications
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You would like to construct a 95% 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 4 degrees Fahrenheit.

(a) What is the best point estimate, based on the sample, to use for the population mean?

☐ degrees

(b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 95% 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 \( t \) | Unclear |
|-----------------------------------------------------------------------------------|---------|---------|------------------------------------|---------|
| The sample has size 100, and it is from a non-normally distributed population.    | ☐       | ☐       | ☐                                  | ☐       |
| The sample has size 16, and it is from a normally distributed population with an unknown standard deviation. | ☐       | ☐       | ☐                                  | ☐       |
| The sample has size 110, and it is from a non-normally distributed population with a known standard deviation of 3.9. | ☐       | ☐       | ☐                                  | ☐       |
Transcribed Image Text:You would like to construct a 95% 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 4 degrees Fahrenheit. (a) What is the best point estimate, based on the sample, to use for the population mean? ☐ degrees (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 95% 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 \( t \) | Unclear | |-----------------------------------------------------------------------------------|---------|---------|------------------------------------|---------| | The sample has size 100, and it is from a non-normally distributed population. | ☐ | ☐ | ☐ | ☐ | | The sample has size 16, and it is from a normally distributed population with an unknown standard deviation. | ☐ | ☐ | ☐ | ☐ | | The sample has size 110, and it is from a non-normally distributed population with a known standard deviation of 3.9. | ☐ | ☐ | ☐ | ☐ |
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