Question

PLEASE ANSWER ALL OF THEM PLEASE

. If we wish to decrease the width of a confidence interval, we may do which one of the following: Change standard deviation of the sample a) b) Reduce size of the population. c) Increase the level of confidence. d) Collect more data. In six test runs, a truck operated 7, 10, 6, 8, 8, and 9 miles with one gallon of gasoline. At the 98% level of confidence, is this sufficient evidence to show that the truck can operate at a mean rate of 9.0 miles per gallon? a) Yes, because confidence interval is about 6 to 10. b) Yes, because confidence interval is about 5.5 to 10.5 c) Yes, because confidence interval is about 6.5 to 9.5. d) No, because confidence interval is about 7.5 to 8.5. A counselor at a community college claims that the mean GPA for students who have transferred to State University is about 2.9. A random sample of 25 such students had a mean GPA of 3.2 with a standard deviation of0.6. Test the counselor's claim at the 99% level ofconfidence. a) Yes. The counselor's claim is valid. b) No. The counselor's claim is not valid. c) both a and b are correct, depending on the total number of students transferred to State University d) both a and b are correct, depending on if data is quantitative or qualitative.

Answer 1

If we wish to decrease the width of a confidence interval, we may collect more data.

If we collect more data, we become more confident about the information we have and hence the width of the confidence interval decreases.

We know that

the number of samples,n =6

sample mean, xbar= (7+10+6+8+8+9) / 6

= 48 / 6

= 8

sample standard deviation= 1.414214

We know that confidence interval

= xbar- t_5,0,_0.01 * s / sqrt(n) , xbar+ t_5,0,_0.01 * s / sqrt(n)

= 8 - 3.364762 * 1.414214 / 2.44949 , 8 + 3.364762 * 1.414214 / 2.44949

= 8 - 3.364762 * 0.5773504 , 8 + 3.364762 * 0.5773504

= 6.057353 , 9.942647 ~ 6,10

Thus, the answer is Yes, because the confidence interval is 6 to 10.

We know that the sample mean, xbar is 3.2.

Also, the sample standard deviation, s is 0.6.

We also know that the sample size, n is 25.

We know that confidence interval

= xbar- t_24,0,_0.005 * s / sqrt(n) , xbar+ t_5,0,_0.005 * s / sqrt(n)

= 3.2 - 3.090513 * 0.6 / 5 , 3.2 + 3.090513 * 0.6 / 5

= 3.2 - 0.3708616 , 3.2 + 0.3708616

= 2.829138, 3.570862

Thus, since the counselor's claim lies within the confidence interval, the answer is Yes. The counselor's claim is valid.