Construct the 99% confidence interval for the difference μ₁-₂ when x₁=476.88, x₂=318.32, s₁=42.11, s₂=26.80, n₁ = 19, and n₂ = 22. Use tables to find the critical value and round the answers to at least two decimal places. A 99% confidence interval for the difference in the population means is 0
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- 11% of all Americans suffer from sleep apnea. A researcher suspects that a different percentage of those who live in the inner city have sleep apnea. Of the 344 people from the inner city surveyed, 34 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.01? The test statistic= (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.)Both, the Cohen's d and confidence interval, measure the impact of the IV on the DV. The only difference is that the confidence interval does so for the population, whereas the Cohen's d does so for the sample.Suppose X1,..., Xn is a random sample from an exponential distribution with mean e. If X = 17.9 with n = 50, find (a) a one-sided 95% confidence interval for 0, and (b) a two-sided 95% confidence interval for 0.
- Step 3 The necessary value for Za/2 was determined to be 1.645. Recall the given information. Sample 1 n1 = 400 P1 = 0.56 P2 = 0.41 Substitute these values to first find the lower bound for the confidence interval, rounding the result to four decimal places. P₁(1-P₁) P₂(1-P₂) 1 72 lower bound = P₁-P₂-²a/2 = 0.560.41 Sample 2 n2 = 300 = 0.0559 = 0.56 0.41 = 02441 X Substitute these values to find the upper bound for the confidence interval, rounding the result to four decimal places. P₁(1-P₁) P₂(1-P₂) upper bound = P₁ P₂ + ²a/2√ n1 n2 X + ✔ - 1.645, + 0.56(1 0.56) 0.41(10.41) 300 +1.645. 400 0.56(1 0.56) + 400 + 0.41(1 0.41) 300Using R Here we will investigate the “confidence level” of each of the confidence intervals:percentile, normal, basic, and BCa. The confidence level of a confidence interval is the longrun proportion that the interval contains the parameter. So, if we took 100 samples andcomputed a 95% CI that estimates the population mean mu, the intervals should contain it95% (95 out of 100) of the time.1(a). Simulate samples X of size n=10 from an exponential distribution with rate =1/50. Run a bootstrap procedure to estimate the median. Compute the 4 CI’s mentionedabove. Repeat this 1,000 times and estimate the confidence level of each type of confidenceinterval.1(b). Are the confidence intervals below or above the confidence level of .95? Whydo you think this is? Explain.1(c). Repeat this for samples of size n=50.1(d). Did the confidence level of the intervals change with the sample size? Are theconfidence intervals below or above the confidence level of .95? Why do you think this…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 is not known, and the histogram of 59 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,…
- A telephone poll of 841 adult Americans was reported in an issue of Time Magazine. One of the questions asked was, "What is the main problem facing the country?" Forty percent answered, "crime." Construct a 88% confidence interval for the population proportion of Americans who feel that crime is the main problem.p'=α2=zα2=Margin of Error: E=We are 88% confident that the proportion of Americans who feel that crime is the main problem is between____ and ____.6.2.3 Find the critical value t, for the confidence levelc=0.99 and sample size n= 12. Click the icon to view the t-distribution table. (Round to the nearest thousandth as needed.)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=3473 thousand dollars, and the histogram of 56 player salaries (in thousands of dollars) of football players on a team is as shown. 040008000120001600020000010203040Salary (thousands of dollars)Frequency 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.
- the powerball lottery is played twice each week in 31 states, the district of columbia and the virgin islands. To play powerball, a participant must purchase a $2 ticket, selest five numbers from the digits 1 through 59, and then select a powerball number from the digits 1 through 35. To determine the winning numbers for each game, lottery officials draw 5 white balls out of a drum of 59 white balls numbered 1 through 59 and 1 red ball out of a drum of 35 red balls numbered 1 through 35. To win the powerball jackpot, a participant's numbers must match the numbers on the 5 white balls in any order and must also match the number on the red powerball. The numbers 5-16-22-23-29 with a powerball number 6 provided the record jackpot of $580 million a) How many powerball lottery outcomes are possible?( hint Consider this a two-step exsperiment. Select the 5 white ball numbers and then selectthe 1 red Powerball number) b) What is the probability that a $2 lottery ticket wins the powerball…IF n < 30 AND T = Ý−µ -H, √n SHOW HOW THE 100(1-2x)% CONFIDENCE INTERVAL FOR U IS DERIVEDA sample of n = 7 scores is selected from a population with an unknown mean ( µ). The sample has a mean of M = 40 and a variance of s 2 = 63. Which of the following is the correct 95% confidence interval for µ?