# Statistics - Confidence Interval and Hypothesis Testing

1.A study with 36 observations had a mean of 70. Assume that the standard deviation is 12. Make a diagram that illustrates the effect of the confidence level on the width of the interval. Use 80%, 90%, 95% and 99%. Summarize what the diagram shows.

2.Computers in some 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 one vehicle equipped in this way, the mpg was recorded each time the gas tank was filled, and the computer was then reset. Here are the mpg values for a random sample of 20 of these records ...

3. The one-sample t statistic for testing ...

(Please see the attached file).

© BrainMass Inc. brainmass.com June 3, 2020, 9:55 pm ad1c9bdddfhttps://brainmass.com/statistics/hypothesis-testing/determining-confidence-interval-hypothesis-testing-205715

#### Solution Preview

The solution file is attached.

1. A study with 36 observations had a mean of 70. Assume that the standard deviation is 12. Make a diagram that illustrates the effect of the confidence level on the width of the interval. Use 80%, 90%, 95% and 99%. Summarize what the diagram shows.

μ = 70, σ = 12, n = 36

x = μ ± z(σ/√n)

x = 70 ± (12/√36) = 70 ± z(2)

∴ xL = 70 - 2z and xR = 70 + 2z

(a) 80% CI (z = 1.2816)

(b) 90% CI (z = 1.645)

(c) 95% CI (z = 1.95)

(d) 99% CI (z = 1.576)

From the ...

#### Solution Summary

Complete, neat and step-by-step solutions regarding the confidence interval and hypothesis testing are provided in the attached file.