Question

1. Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value tα/2​, ​(b) find the critical value zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies.

The confidence level is 95​%, σ=3999 thousand​ dollars, and the histogram of 66 player salaries​ (in thousands of​ dollars) of football players on a team is as shown.

0

4000

8000

12000

16000

20000

0

10

20

30

40

Salary (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, 36; 2000, 16; 4000, 2; 6000, 4; 8000, 2; 10000, 4; 12000, 0; 14000, 0; 16000, 1; 18000, 0; 20000, 1.

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

A.

tα/2= nothing

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

B.

zα/2= nothing

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

C.

Neither the normal distribution nor the t distribution applies.

2.Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4466 patients treated with the​ drug, 122 developed the adverse reaction of nausea. Construct a 99​% confidence interval for the proportion of adverse reactions.

​a) Find the best point estimate of the population proportion p.

nothing

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

Answer 1

Given 1. n = 66 = 3999 (in thousand dollars) Confidence level = 95% = 0.95 since, n730 7 According to central limit theorm, the distribution of sample mean may be as normal distribution. so, we go for Z-test, approximated Here, L = 1-0.95 = 0.05 13 Hr 0.025 1.96 2 20.025 Ans. CHA XH2 s 2.00 from to distribution table = 2.00 Answers Aở to, 2 0 0 1. 96 Ans- Za > Normal distribution applies (Although population looks so we can conclude that neither the normal nor the Z-distribution applies.. very skewed

CO 30 frequency Shop 20t 10 2000 2010 10000 2000 MOVID 18000 18010 4000 6000 8000 Salary &000

2 Given ne 4466 X 21 22 Cmfidence iwel - 99% = 0.99 102 Best point estimate of the population properton – sample proponin ľ z sample proportion Pa 122 z 0.027 4466 1- 0.99 = 0.01 P. 0.01 = 0.005 nola c z n Za ala 2.oos = 2.375 from 2-table) Standard emona PLI-P) 10.027(1-0-027) 50.0024 4466 Margin of error emor a PUP) 22. S75X 0.0024 = 0.00618 Confidence interval: Far & t margin of assor 1027 +.00618 [ - 02.082, 0.03318] And True proportion of adverse reaction in the population lies in the given interval. (garr. Confident