The sample mean and standard deviation from a random sample of 25 observations from a normal population were computed as $x̄ = 40$ and $s = 14$. Calculate the t statistic of the test required to determine whether there is enough evidence to infer at the 2% significance level that the population mean is greater than 38.

Test Statistic = ___ Answer : Given : The sample mean $(x̄) = 40$ The sample standard deviation $(s) = 14$ The sample size $(n) = 25$ The significance level $(α) = 0.02$ Solution : The null and alternative hypothesis,…

The college bookstore tells prospective students that the average cost of its textbooks is 60 and less, with a standard deviation of 4.50. A group of smart statistics students thinks that the average cost is higher. In order to test the bookstore’s claim against their alternative, the students will select a random sample of size 100. Assume that the mean from their random sample is 60.20. Perform a hypothesis test at the 10% level of significance and state your decision.

Answer : Given : Sample mean $(x\bar) = 60.2$ Population standard deviation $(σ) = 4.5$ Sample size $(n) = 100$ Significance level $(α) = 0.10$ Solution : The null and alternative hypothesis, $H_0 : \mu \leq 60$ $H_1 : \mu…

An old medical textbook states that the mean sodium level for healthy adults is 138 mEq per liter of blood. A medical researcher believes that, because of modern dietary habits, the mean sodium level for healthy adults, μ, now differs from that given in the textbook. A random sample of 50 healthy adults is evaluated. The mean sodium level for the sample is 140 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 11 mEq/L. Can we conclude, at the 0.05 level of significance, that the population mean adult sodium level now differs from that given in the textbook?

Perform a two-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.) (a) State the null hypothesis H0​ and…

The mean SAT score in mathematics is 596. The standard deviation of these scores is 25. A special preparation course claims that the mean SAT score, μ\muμ, of its graduates is greater than 596. An independent researcher tests this by taking a random sample of 90 students who completed the course; the mean SAT score in mathematics for the sample was 597. At the 0.05 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 596? Assume that the population standard deviation of the scores of course graduates is also 25.

Perform a ______ 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.) (a) State the null hypothesis $(H_0)$ and…

Hours Dogs Sleep The Canadian Press reported that dogs sleep on average 14 hours per day. A veterinarian studied a random sample of 50 dogs and found that they sleep on average 15.4 hours. The standard deviation of the population, which was 1.7 hours, was found from previous studies. At α=0.10\alpha = 0.10α=0.10, can it be concluded that on average dogs sleep more than 14 hours per day? Assume the variable is normally distributed. Use the critical value method.

(a) State the hypotheses and identify the claim with the correct hypothesis. $H0​:μ=14 $ (not claim) $H1​:μ>14 $ (claim) This hypothesis test is a _____ test. (b) Find the critical value(s). Round the answer(s) to at least two decimal places.…