1. Randomly selected 17 student cars have ages with a mean of 7.7 years and a st

Question

1. Randomly selected 17 student cars have ages with a mean of 7.7 years and a standard deviation of 3.4 years, while randomly selected 30 faculty cars have ages with a mean of 5 years and a standard deviation of 3.7 years.

-Construct a 99% confidence interval estimate of the difference sf, where s is the mean age of student cars and f is the mean age of faculty cars.

2. A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. An SRS of 25 stores this year shows mean sales of 59 units of a small appliance, with a standard deviation of 7.8 units. During the same point in time last year, an SRS of 10 stores had mean sales of 51.434 units, with standard deviation 9.4 units. An increase from 51.434 to 59 is a rise of about 13%.

-Construct a 95% confidence interval estimate of the difference 12, where 1 is the mean of this year's sales and 2 is the mean of last year's sales.

-The margin of error....?

3. In a study of red/green color blindness, 500 men and 2850 women are randomly selected and tested. Among the men, 44 have red/green color blindness. Among the women, 9 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.

-Construct the 99% confidence interval for the difference between the color blindness rates of men and women.

Explanation / Answer

1)

n1 = 17 , x1 = 7.7 , s1 = 3.4 , n2 = 30 , x2 = 5 , s2 = 3.7

z value at 99% CI = 2.576

CI = ( x1 - x2 ) + /- z * sqrt ( s1^2 /n1 + s2^2 /n2)

= ( 7.7 - 5) + /- 2.576 * sqrt ( 3.4^2 / 17 + 3.7^2 / 30)
= (-0.0459 , 5.446)

2)

n1 = 25 , x1 = 59 , s1 = 7.8 , n2 = 10 , x2 = 51.434 , s2 = 9.4

z value at 95% CI = 1.96

CI = ( x1 - x2 ) + /- z * sqrt ( s1^2 /n1 + s2^2 /n2)

= ( 59 - 51.434) + /- 1.96 * sqrt ( 7.8^2 / 25 + 9.4^2 / 10)
= (0.986 , 14.145)

3)
n1 = 500 , p1 = 44/500 =0.088 , n2 = 2850 , p2 = 9 /2850= 0.003
z value at 99% CI = 2.576

CI = ( p1 - p2 ) + /- z * sqrt ( p1 (1-p1) /n1 + p2 (1-p2) /n2)

= ( 0.088 - 0.003) + /- 2.576 * sqrt ( 0.088*0.912 / 500 + 0.003 * 0.997 / 2850)
= (0.052 , 0.117)
  

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