# Confidence Intervals

Confidence Intervals on SPSS®

Do the following confidence intervals on SPSS®. Your printouts are to be exported into Word as demonstrated on the Tegrity Video SPSS Confidence Intervals. Give only the interpretations of the confidence interval, double spaced. Do not include the questions. DO NOT REMOVE DECIMALS FROM THE DATA. When writing the interpretations for the confidence intervals, do not round your answers.

1. A consumer testing service wants to study the noise level of a new vacuum cleaner. Measuring the noise level of a random sample of 12 machines, it gets the following data (in decibels). Find a 95% confidence interval for the average noise level of such vacuum cleaners. Do not round the final answer. Enter the data with 1 decimal place.

74.0     78.6     76.8     75.5     73.8     75.6     77.3     75.8     73.9     70.2     81.0     73.9

1. Computers in some economy size vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For 20 economy size vehicles equipped in this way, the mpg was recorded each time the gas tank was filled and the computer was then reset. What is a 99% confidence interval for the average mpg? The following are the mpg values for these vehicles. Do not round the final answer. Enter the data with one decimal place.

41.5     50.7     36.6     37.3     34.2     45.0     48.0     43.2     47.7     42.2

43.2     44.6     48.4     46.4     46.8     39.2     37.3     43.5     44.6     43.3

Solution

T-Test Ryan

[DataSet1]

 One-Sample Statistics N Mean Std. Deviation Std. Error Mean noise 12 75.533 2.7506 .7940
 One-Sample Test Test Value = 0 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper noise 95.125 11 .000 75.5333 73.786 77.281

T-Test

[DataSet2]

 One-Sample Statistics N Mean Std. Deviation Std. Error Mean mpg 20 43.185 4.4195 .9882
 One-Sample Test Test Value = 0 t df Sig. (2-tailed) Mean Difference 99% Confidence Interval of the Difference Lower Upper mpg 43.699 19 .000 43.1850 40.358 46.012

………

1. It can be stated with 95% confidence that the average noise level of the new vacuum cleaner that is being tested is between 73.786 and 77.281 decibels.
1. It can be stated with 99% confidence that the average fuel efficiency or gas mileage of the economy size vehicles is between 40.358 and 46.012 miles per gallon (mpg).