The mean SAT score in mathematics is 537. The standard deviation of these scores is 31. A special preparation course claims that the mean SAT score, µ, of its graduates is greater than 537. An independent researcher tests this by taking a random sample of 70 students who completed the course; the mean SAT score in mathematics for the sample was 547. At the 0.01 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 537? Assume that the population standard deviation of the scores of course graduates is also 31. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) Español ? (a) State the null hypothesis H and the alternative hypothesis H₁. H₁ : 0 Ho H₁:0 (b) Determine the type of test statistic to use. μ 0 р x S t Degrees of freedom: ロ=ロ □□ □□ (c) Find the value of the test statistic. (Round to three or more decimal places.) □≠□ □<□ O

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 84 and a standard deviation of 6. The professor has informed us that 10 percent of his students received A's while only 2.5 percent of his students failed the course and received F's.   a. To the nearest tenth, what is the minimum score needed to make an A?   b. To the nearest tenth, what is the maximum score among those who received an F?   c. If there were 4 students who did not pass the course, how many students took the course?

The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 17.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds?

Steve believes that his wife's cell phone battery does not last as long as his cell phone battery. On eleven different occasions, he measured the length of time his cell phone battery lasted and calculated that the mean was 16.4 hours with a standard deviation of 6.4 hours. He measured the length of time his wife's cell phone battery lasted on seven different occasions and calculated a mean of 23.3 hours with a standard deviation of 4.2 hours. Assume that the population variances are the same. Let Population 1 be the battery life of Steve's cell phone and Population 2 be the battery life of his wife's cell phone. Step 1 of 2: Construct a 90 % confidence interval for the true difference in mean battery life between Steve's cell phone and his wife's. Round the endpoints of the interval to one decimal place, if necessary.