A pharmaceutical company manufactures a 81-mg pain reliever. Company specifications include that the standard deviation of the amount of the active ingredient is 2 mg. The quality-control manager selects a random sample of 30 tablets from a certain batch and finds that the standard deviation is 2.4 mg. Assume that the amount of the active ingredient is normally distributed. Test the claim that the standard deviation of the amount of the active ingredient is greater than 2 mg at the a = 0.05 level of significance. Test Statistic = Don't round. Keep all digits. %3D P-Value Round to thousandths place. Decision Write "Reject" or "Fail to Reject"

The mean number of close friends for the population freshman college students in the U.S.A. is u 5.7. The standard deviation of scores in this population is 1.3. A psychologist predicts that the mean number of close friends for freshman introverts will be significantly different from the mean of the population. The mean number of close friends for a random sample of 25 freshman introverts is M = 6.5. Set your alpha level at a = .05. Complete steps 3 and 4 of the hypothesis testing procedure. What decision should the researcher make regarding the effect of introversion on the number of close friends? = O The researcher should retain Ho and conclude that introversion has no effect on the number of close friends. The researcher should retain HA and conclude that introversion has no effect on the number of close friends. O The researcher should reject Ho and conclude that introversion makes a difference in the number of close friends one has. O The researcher should reject HA and conclude…

The United States ranks ninth in the world in per capita chocolate consumption; Forbes reports that the average American eats 9.5 pounds of chocolate annually. Suppose you are curious whether chocolate consumption is higher in Hershey, Pennsylvania, the location of the Hershey Company's corporate headquarters. A sample of 35 individuals from the Hershey area showed a sample mean annual consumption of 10.05 pounds and a standard deviation of s = 1.5 pounds. Using α = 0.05, do the sample results support the conclusion that mean annual consumption of chocolate is higher in Hershey than it is throughout the United States?   State the null and alternative hypotheses. (Enter != for ≠ as needed.) H0:_________________   Ha:__________________   Find the value of the test statistic. (Round your answer to three decimal places.) _____________________.   Find the p-value. (Round your answer to four decimal places.) p-value =____________________.   State your conclusion.(multiple choice) A.…

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is u = 7.4.t A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.1. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. (a) What is the level of significance? State the null and alternate hypotheses. О но: и 3 7.4;B н,: и 7.4; Η: μ = 7.4 Ο H μ= 7.4; H : μ > 7.4 О но: и+ 7.4; н:и3 7.4 O Ho: H = 7.4; H,: µ # 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is unknown. O The Student's t,…