Question

PLEASE ANSWER ALL QUESTIONS

1. What z value is used with a 98% confidence level?

Select one:

a. 1.65

b. 1.96

c. 1.28

d. 2.33

2. What z value is used with a 75% confidence level?

Select one:

a. 1.15

b. 1.56

c. 1.37

d. 0.90

e. 1.88

f. 2.17

g. 0.99

h. 2.05

3. You are studying the effects of two diets on young adults. You measure the weight of students before and after an eight week diet program. In 50 students participating in diet Alpha, the average weight loss is 4.6 pounds with a standard deviation of 2.2 pounds. In 50 students participating in diet Bravo, the average weight loss is 9.8 pounds with a standard deviation of 3.6 pounds. You construct a 95% confidence interval for the change in weight for diet Alpha and another 95% confidence interval for the change in weight for diet Bravo. Which confidence interval is wider?

Select one:

a. Diet Alpha has a wider 95% confidence interval than Diet Bravo.

b. Diet Bravo has a wider 95% confidence interval than Diet Alpha.

c. Diet Alpha and Diet Bravo have equally wide confidence intervals.

Answer 1

Solution :

Given that,

1) At 98% confidence level

= 1-0.98% =1-0.98 =0.02

/2 =0.02/ 2= 0.01

Z/2 = Z_{0.01 = 2.326}

Z/2 = 2.326 = 2.33

d. 2.33

2)

At 75% confidence level

= 1-0.75% =1-0.75 =0.25

/2 =0.25/ 2= 0.125

Z/2 = Z_{0.125 = 1.15}

Z/2 =1.15  

a. 1.15

3) a) Aipha

Point estimate = sample mean = = 4.6

Population standard deviation = = 2.2

Sample size = n = 50

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.025 = 1.960}

Z/2 = 1.960  

Margin of error = E = Z/2 * ( /n)

= 1.960 * (2.2 /  50 )

= 0.61

At 95 % confidence interval estimate of the population mean is,

- E < < + E

4.6 - 0.61 <   < 4.6 + 0.61

3.99<   < 5.21

( 3.99 , 5.21 )

B) BRAVO

Point estimate = sample mean = =9.8

Population standard deviation = = 3.6

Sample size = n = 50

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.025 = 1.960}

Z/2 = 1.960  

Margin of error = E = Z/2 * ( /n)

= 1.960 * (3.6 /  50 )

= 0.998

At 95 % confidence interval estimate of the population mean is,

- E < < + E

9.8 - 0.998 <   < 9.8 + 0.998

8.802<   < 10.798

( 8.802 , 10.798 )

c. Diet Alpha and Diet Bravo have equally wide confidence intervals.