The Acme Company has developed a new battery. The engineer in charge claims that the new battery will operate continuously for at least 7 minutes longer than the old battery. To test the claim, the company selects a simple random sample of 100 new batteries and 100 old batteries. The old batteries run continuously for 190 minutes with a standard deviation of 20 minutes; the new batteries, 200 minutes with a standard deviation of 40 minutes. Test the engineer's claim that the new batteries run at least 7 minutes longer than the old. Use a 0.05 level of significance. (Assume that there are no outliers in either sample.) a. Null hypothesis and alternative hypothesis b. Test statistic to be used, appropriate critical region and actual value of the test statistic c. Statistical decision and statistical conclusion

Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2.   Step 2 of 3 :   Compute the value of the test statistic. Round your answer to two decimal places.

The null hypothesis: H, :0 The alternative hypothesis: H :0 The type of test statistic: (Choose one) v The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.05 level of significance: (Round to at least three decimal places.) Can we support the claim that the life expectancy in the United States is greater than the life expectancy in Ireland? O Yes No

Nintendo is doing a classic game competition for the anniversary of Super Mario Bros. The average runtime for a straight playthrough is 1 hour and 58 minutes (with a standard deviation of 6 minutes). Out of all of the players who compete in this competition (120 players), the fastest 10% will get a chance at a special reward. What would be the benchmark playthrough time for this competition?

The human resources department of a consulting firm gives a standard creativity test to a randomly selected group of new hires every year. This year, 100 new hires took the test and scored a mean of 113.6 points with a standard deviation of 134. Last year, 95 new hires took the test and scored a mean of 116.4 points with a standard deviation of 16.8. Assume that the population standard deviations of the test scores of all new hires in the current year and the test socores of all new hires last year can be estimated by the sample standard deviations, as the samples used were quite large. Construct a 90 confidence interval for the difference between the mean test score , of new hires from the current year and the mean test score , of new hires from last year. Then tind the lower limit and upper limit of the 905% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answeis to at least two decimal places. (If necessary, cosult a list.ot…

Two estimates are available for the same population parameter. Estimate one has a standard deviation of 8.5 and estimate two has a standard deviation of 8.7. Estimate two is unbiased, whereas estimate one is biased. Which estimate would you choose and why?

According to the historical data, the life expectancy in the United States is less than or equal to the life expectancy in Ireland. A new study has been made to see whether this has changed. Records of 235 individuals from the United States who died recently are selected at random. The 235 individuals lived an average of 77.6 years with a standard deviation of 6.7 years. Records of 220 individuals from Ireland who died recently are selected at random and independently. The 220 individuals lived an average of 76.3 years with a standard deviation of 5.5 years. Assume that the population standard deviations of the life expectancies can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.1 level of significance, is there enough evidence to support the claim that the life expectancy, u,, in the United States is greater than the life expectancy, µ, in Ireland? Perform a one-tailed test. Then fill in the table below. Carry…

Two chemical companies can supply a raw material. The concentration of a particular element in this material is important. The mean concentration for both suppliers is the same, but you suspect that the variability in concentration may differ for the two companies. The standard deviation of concentration in a random sample of n₁ = 10 batches produced by company 1 is s₁ = 4.7 grams per liter, and for company 2, a random sample of n₂ = 16 batches yield s₂ = 5.8 grams per liter. Is there sufficient evidence to conclude that the two populations variances differ? Use a = 0.05. a. Because 0.321 < 0.657 <3.77, fail to reject the null hypothesis b. Because 0.265 < 0.657 <3.12, fail to reject the null hypothesis c. Because 0.386 < 0.657 <3.01, fail to reject the null hypothesis d. None among the choices

A newly hired basketball coach promised a high- paced attack that will put more points on the board than the team's previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach's claim. He takes a sample of 36 of the team's games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is(are) the appropriate critical value(s) to test the new coach's claim at the 1% significance level? -2.438 -2.438 and 2.438 2.326 2.438

times for a surgical procedure are normally distributed. there are two methods. method a has a mean of 29 minutes and a standard deviation of 5 minutes, while method b has a mean of 33 minutes and a standard deviation of 25 minutes. which procedure is preferred if the procedure must be completed within 37 minutes. method a, b, or either method