One Population Mean Confidence Interval

A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...

• The t distribution is more accurate than a z distribution.

• Clarity ratings for the entire bacth are normally distributed.

• The t-distribution will create a narrower interval than z.

• The standard deviation for the population is unknown.

The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were: 13.2,  5.1,  7.5,  8.0,  12.7,  7.6,  13.8,  14.5,  7.7, and 10.5.  Determine a 95 percent confidence interval for the mean time for all players.

• 12.30 < μ < 7.82

•  7.82 < μ < 12.30

• 7.72 < μ < 12.40

• 12.40 < μ < 7.72

A sample of 40 people owned an average of 1.35 apple products. It is known from a previous study that the population standard deviation of apple product ownership is 0.63 products. Construct a 95% confidence interval.

• (1.11, 1.58)

• (1.15, 1.55)

• (1.19, 1.51)

• (1.09, 1.61)

A local bank needs information concerning the savings account balances of its customers. A random sample of 13 accounts was checked. The mean balance was $686.75 with a sample standard deviation of $256.20. Find a 95% confidence interval for the true mean.

• ($513.14, $860.36)

• ($525.59, $847.91) 

• ($533.27, $840.23)

• ($531.92, $841.58)

Which of the following changes to a study would result in a smaller confidence interval?

• increasing the confidence level, increasing the sample size

• increasing the confidence level, decreasing the sample size

• decreasing the confidence level, decreasing the sample size

• decreasing the confidence level, increasing the sample size.

What is the margin of error for the interval (6.8, 12.9)?

• 9.85

• 3.05

• 3.50

• 6.8

Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%

• 95%

• 98%

• 99%

The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter.

• True

• False

Find the value of z_c for a 90% confidence interval.

• -1.96 

• 1.645

• 1.440

• -1.598

Find the 95% confidence interval if the mean is 10 and the margin of error is ±2 .

• ±2

• ±95

• ±10

• ±2