Confidence Interval for a Mean, Sigma Known

The scores of a random sample of 100 high school students on a standardized mathematics test in school A gave a mean of 78 and a standard deviation of 20. Find the 95% confidence interval estimate for the true average score in mathematics in this standardized test.

• 1.96 to 3.92

• 76 to 80

• 74.08 to 81.92

• 74.80 to 81.29

A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the population standard deviation of the contents is 0.22 ounces. In this problem, the 4 ounces is?

• A parameter

• A statistic

• The standard error of the mean

• The average content of colognes in the long run

When a 99% confidence interval is calculated instead of a 95% confidence interval with n being the same, the maximum error of estimate will be?

• smaller

• larger

• the same

• not be determined

The scores of a random sample of 100 high school students on a standardized mathematics test in school A gave a mean of 78 and a standard deviation of 20. What is the best point estimate of the true average score in this standardized mathematics test?

• 20

• 78

• 95

• 100

A random sample of 100 visitors to a popular theme park spent an average of $142 on the trip with a standard deviation of $47.5. Which of the following would be the 98% confidence interval for the mean money spent by all visitors to this theme park?

• ($130.77, $153.23)

• ($132.77, $151.43)

• ($132.69, $151.31)

• ($140.88, $143.12)

You sample 12 bugs and find the sample mean is 2.40 cm. You are told the standard deviation is 0.2 cm. Find a 95% Confidence Interval.

• 1.96

• n

• 12

• σ

• 2.40

• μ

• .2

• Z

You sample 12 bugs and find the sample mean is 2.40 cm. You are told the standard deviation is 0.2 cm. Find a 95% Confidence Interval.

• 2.40

• σ

• 1.96

• n

• .2

• Z

• 12

• μ

A random sample of 100 visitors to a popular theme park spent an average of $142 on the trip with a sample standard deviation of $47.50. Which of the following would be the 98% confidence interval for the mean money spent by all visitors to this theme park?

• 
  ($130.77, $153.23)

• 
  ($132.69, $151.31)

• 
  

  ($130.96, $153.07)

• 
  ($140.88, $143.12)

You are testing chocolate chip cookies to estimate the mean number of chips per cookie. You sample 25 cookies and you find a sample mean of 10 chips per cookie and a standard deviation of 2. Find a 95% confidence interval. Which of the following is incorrect?

• μ = 25

• σ = 2

• Z = 1.96

• n = 25

We measure the height of 40 randomly selected women, in which the mean height is 175cm. We also know the population standard deviation is 20cm. Which of the following represents a 95% Confidence Interval?

• 175cm ±1.645* 3.16

• 175cm ± 1.96*3.16

• 175cm ± 1.96*20

• 175cm ± 1.645*40