Module 4 Exercise 2

True or False. The population mean is always enclosed by the confidence interval estimate.

• True

• False

True or False: If two confidence interval estimates were constructed from the same sample, the wider interval has the lower confidence level.

• True

• False

A nutritionist wants to estimate the average calorie content of the burritos at a popular restaurant. They obtain a random sample of 140 burritos and measure their calorie content. Their sample data are roughly symmetric with a mean of 700 calories and a standard deviation of 50 calories.

Determine the margin of error for a 90% confidence interval. (2 d.p.)

• 6.95

• 8.28

• 32.57

• 97.32

A nutritionist wants to estimate the average calorie content of the burritos at a popular restaurant. They obtain a random sample of 140 burritos and measure their calorie content. Their sample data are roughly symmetric with a mean of 700 calories and a standard deviation of 50 calories.
Construct a 90% confidence interval for the mean calorie content of these burritos. 

•  $602.68<\mu<797.32$  
  

•  $691.72<\mu<708.28$  

•  $667.43<\mu<732.57$  

•  $693.05<\mu<706.95$  
  

A random sample of 10 chocolate energy bars of a certain brand has, on the average, 230 calories with known population standard deviation of 15 calories. Assume that the distribution of calories is approximately normal.

Determine a point estimate for the true mean calorie content of this brand of energy bar.

A random sample of 10 chocolate energy bars of a certain brand has, on the average, 230 calories with known population standard deviation of 15 calories. Assume that the distribution of calories is approximately normal.

Find the margin of error for a 95% confidence interval.

(2 d.p.)

A random sample of 10 chocolate energy bars of a certain brand has, on the average, 230 calories with known population standard deviation of 15 calories. Assume that the distribution of calories is approximately normal.

Construct a 95% confidence interval for the true mean calorie content of this brand of energy bar.

(2 d.p.)

• $222.20<\mu<237.80$

• $220.70<\mu<239.30$
  

• $217.79<\mu<242.21$

A commonly used IQ test has a standard deviation of 15. A school counselor was curious about the average IQ of the students in her school and took 100 random samples of forty students’ IQ scores. The average of these scores was 107.9.

 $What\ is\ the\ \overline{x}\ ?$  

A commonly used IQ test has a standard deviation of 15. A school counselor was curious about the average IQ of the students in her school and took 100 random samples of forty students’ IQ scores. The average of these scores was 107.9.

Determine the critical z-score value for a 99% confidence interval.

A commonly used IQ test has a standard deviation of 15. A school counselor was curious about the average IQ of the students in her school and took 100 random samples of forty students’ IQ scores. The average of these scores was 107.9.

Find a 99% confidence interval for the mean student IQ in the school. (Round off the margin of error to 2 d.p. before constructing the interval.)

•  $93.89<\mu<106.11$ 

•  $101.79<\mu<114.01$ 

•  $96.14<\mu<103.86$ 

•  $104.04<\mu<111.76$