**Question**

Suppose that the number of dollars spent per week on groceries are normally distributed with an unknown mean and standard deviation. A random sample of 18 grocery bills is taken and gives a sample mean of 103 dollars and a sample standard deviation of 10 dollars.

The margin of error for a 98% confidence interval estimate for the population mean using the Student’s t-distribution is 6.05. Find a 98% confidence interval estimate for the population mean using the Student’s t-distribution.

- Round the final answers to two decimal places.

# Question

Suppose that the number of dollars spent per week on groceries are normally distributed with an unknown mean and standard deviation. A random sample of 18 grocery bills is taken and gives a sample mean of 103 dollars and a sample standard deviation of 10 dollars.

# Question

Suppose that the amount of sleep, in hours, obtained per night by healthy adults is normally distributed with an unknown population mean and standard deviation. If a random sample of 36 healthy adults is taken to estimate the mean nightly amount of sleep, what t-score should be used to find a 95% confidence interval estimate for the population mean?

**Question**

The speeds of vehicles traveling on a highway are normally distributed with an unknown population mean and standard deviation. If a random sample of 38 vehicles is taken to estimate the mean vehicle speed, what t-score should be used to find a 99% confidence interval estimate for the population mean?

# Question

The weights of running shoes are normally distributed with an unknown population mean and standard deviation. If a random sample of 23 running shoes is taken and results in a sample mean of 12 ounces and sample standard deviation of 3 ounces, find a 95% confidence interval estimate for the population mean using the Student’s t-distribution.

# Question

The weights of running shoes are normally distributed with an unknown population mean and standard deviation. If a random sample of 23 running shoes is taken and results in a sample mean of 12 ounces and sample standard deviation of 3 ounces, find the margin of error, ME, for a 95% confidence interval estimate for the population mean using the Student’s t-distribution.

# Question

Suppose the wait times for patients in an emergency room are normally distributed with an unknown population mean and standard deviation. If a random sample of 31 emergency room patients is taken to estimate the mean wait time, what t-score should be used to find a 98% confidence interval estimate for the population mean?

**Question**

The commute times for workers in a city are normally distributed with an unknown population mean and standard deviation. If a random sample of 20 workers is taken and results in a sample mean of 21 minutes and sample standard deviation of 6 minutes, find a 95% confidence interval estimate for the population mean using the Student’s t-distribution.

The margin of error for a 95% confidence interval estimate for the population mean using the Student’s t-distribution is 2.81. Find a 95% confidence interval estimate for the population mean using the Student’s t-distribution.

- Round the final answers to two decimal places.

# Question

The commute times for workers in a city are normally distributed with an unknown population mean and standard deviation. If a random sample of 20 workers is taken and results in a sample mean of 21 minutes and sample standard deviation of 6 minutes, find a 95% confidence interval estimate for the population mean using the Student’s t-distribution.

Find the margin of error, for a 95% confidence interval estimate for the population mean using the Student’s t-distribution.

- Use the portion of the table above. Round the final answer to two decimal places.

# Question

Suppose that the exam scores for students in a large university course are normally distributed with an unknown mean and standard deviation. The scores of 42 randomly sampled students in the course are used to estimate the mean of the population. What t-score should be used to find the 99% confidence interval for the population mean?

**Solution:**

**Question**

Suppose that the number of dollars spent per week on groceries are normally distributed with an unknown mean and standard deviation. A random sample of 18 grocery bills is taken and gives a sample mean of 103 dollars and a sample standard deviation of 10 dollars.

The margin of error for a 98% confidence interval estimate for the population mean using the Student’s t-distribution is 6.05. Find a 98% confidence interval estimate for the population mean using the Student’s t-distribution.

- Round the final answers to two decimal places.

**Correct answers:**

We are 98% confident that the true population mean lies between 96.95 and 109.05

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