Question

Question 11: A genetic experiment with peas resulted in one sample of offspring that consisted of 421 green peas and 157 yellow peas.

a. Construct a 90​% confidence interval to estimate of the percentage of yellow peas. Express the percentages in decimal form.nothingless than<pless than<nothing

b. It was expected that​ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

Question 12: In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 326 accurate orders and 58 that were not accurate.

a. Construct a 90​% confidence interval estimate of the percentage of orders that are not accurate.

b. Compare the results from part​ (a) to this 90​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.136less than<pless than<0.199 What do you​ conclude?

Question 13: A study of 420,075 cell phone users found that 137 of them developed cancer of the brain or nervous system. Prior to this study of cell phone​ use, the rate of such cancer was found to be 0.0319% for those not using cell phones. Complete parts​ (a) and​ (b).

a. Use the sample data to construct a 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

nothing​%less than<pless than<nothing​%

​(Round to three decimal places as​ needed.)

Question 14: A programmer plans to develop a new software system. In planning for the operating system that he will​ use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 99​% confident that his estimate is in error by no more than two percentage points question marks? Complete parts​ (a) through​ (c) below.

​a) Assume that nothing is known about the percentage of computers with new operating systems.

n= ?

​(Round up to the nearest​ integer.)

​b) Assume that a recent survey suggests that about 90​% of computers use a new operating system.

n= ?

​(Round up to the nearest​ integer.)

Question 30:

Assume that we want to construct a confidence interval. Do one of the​ following, as​appropriate: (a) find the critical value t Subscript alpha divided by tα/2​, ​(b) find the critical value z Subscript alpha divided by zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies.The confidence level is 9595​%, sigmaσequals=37223722 thousand​ dollars, and the histogram of 5858 player salaries​ (in thousands of​ dollars) of football players on a team is as shown.

040008000120001600020000010203040Salary (thousands of dollars)Frequency A histogram has a horizontal axis labeled "Salary (thousands of dollars)" from below 0 to above 20000 in increments of 2000 and a vertical axis labeled "Frequency" from 0 to 40 in increments of 10. The histogram contains vertical bars of width 2000, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the salary is listed first and the height is listed second: 0, 34; 2000, 12; 4000, 3; 6000, 2; 8000, 3; 10000, 3; 12000, 0; 14000, 0; 16000, 0; 18000, 0; 20000, 1.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. tα/2= ​(Round to two decimal places as​ needed.)

B.zα/2= (Round to two decimal places as​ needed.)

C.Neither the normal distribution nor the t distribution applies.

Question #31: Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value t Subscript alpha divided by 2tα/2​, ​(b) find the critical value z Subscript alpha divided by 2zα/2​,

or​ (c) state that neither the normal distribution nor the t distribution applies.Here are summary statistics for randomly selected weights of newborn​ girls:n=257, x overbar equals=31.7 ​hg, s=7.97.9 hg. The confidence level is 90​%.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. tα/2= ​(Round to two decimal places as​ needed.)

B.zα/2= (Round to two decimal places as​ needed.)

C.Neither the normal distribution nor the t distribution applies.

Answer 1

Question 11: A genetic experiment with peas resulted in one sample of offspring that consisted of 421 green peas and 157 yellow peas.

a)

n = 421 + 157 = 578

x = 157

P = 157 / 578 = 0.272

90​% confidence interval

α = 0.10

Zα/2 = 1.645

90​% confidence interval = P +/- Zα/2 (√((P*(1-P)) / n))

= 0.272 +/- 1.645 * 0.0185

= 0.272 +/- 0.030

= (0.242 , 0.302)

90​% confidence interval (0.242 , 0.302)

b) No, the confidence interval includes, So the true percentage could easily equal to 25%

Question 12: In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 326 accurate orders and 58 that were not accurate.

a)

n = 326 + 58 = 384

x = 58

P = x/n = 58 / 384 = 0.151

90​% confidence interval

α = 0.10

Zα/2 = 1.645

90​% confidence interval = P +/- Zα/2 (√((P*(1-P)) / n))

= 0.151 +/- 1.645 * 0.1827

= 0.151 +/- 0.301

90​% confidence interval = (-0.15 , 0.452)

Restaurant​ A : -0.15 < p < 0.452

Restaurant​ B: 0.136 < p < 0.199

lower limit of confidence interval for A is less than the lower limit of confidence interval for B

Upper limit of confidence interval for A is greater than the upper limit of confidence interval for B

Significantly different and not accurate

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