A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 747 hours. A random sample of 29 light bulbs has a mean life of 721 hours. Assume the population is normally distributed and the population standard deviation is 58 hours. At a = 0.02, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e). (a) Identify the null hypothesis and alternative hypothesis. O B. Ho: u> 747 Hai us 747 (claim) OC. Ho:H< 721 (claim) Ha: u2 721 O A. Ho: H2 747 (claim) Ha: H<747 O D. Ho:H= 747(claim) O E. Ho: Hs 721 OF. Ho:µ = 721 Hai H = 747 Ha: u> 721 (claim) Hai u = 721 (claim) (b) Identify the critical value(s). Use technology. Zo = (Use a comma to separate answers as needed. Round to two decimal places as needed.) Identify the rejection region(s). Choose the correct answer below. O A. O B. OC. Fail to reject Ho- Fail to reject Ho- Fail to reject Ho- Reject H- Reject Hg- Reject Ho Reject Ho- (c) Identify the standardized test statistic. Use technology. (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. O A. Reject Ho. There is sufficient evidence to reject the claim that mean bulb O B. Reject Ho. There is not sufficient evidence to reject the claim that mean life is at least 747 hours. bulb life is at least 747 hours. OC. Fail to reject Hn. There is sufficient evidence to reject the claim that O D. Fail to reject Hn. There is not sufficient evidence to reject the claim that mean bulb life is at least 747 hours. mean bulb life is at least 747 hours.

A study conducted by Hershey's discovered that Americans consumed an average of 11.4 pounds of chocolate per year. Let's assume that the annual chocolate consumption follows the Normal distribution with mean 11.4 pounds and a standard deviation of 3.6 pounds. Answer the following questions, performing all computations with Excel functions.

Assume the samples are random and independent, the populations are nomally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At a = 0.10, is there enough evidence conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below. E Click the icon to view the battery cost data. (a) Let u1. P2. H3 represent the mean prices for the group size 35, 65, and 24/24F respectively. Identify the claim and state Ho and H. H Cost of batteries by type The claim is the V hypothesis. Group size 35 Group size 65 Group size 24/24F 101 111 121 124 D 146 173 182 278 124 140 141 89 (b) Find the critical value, Fo, and identify the rejection region. 90 79 84 The rejection region is F Fo, where Fo = (Round to two decimal places as needed.) (c) Find the test statistic F. Print Done F= (Round to two decimal places as…

Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) to (c) below. Reduction in Pain Level After Magnet Treatment (μ₁): n = 15, x=0.45, s=1.02 Reduction in Pain Level After Sham Treatment (2): n = 15, x=0.38, s=1.55 a. Use a 0.01 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo). What are the null and alternative hypotheses? OA. Ho H1 H2 oc Hoi HH2 H₁: H1 H2 B. Ho: H1 H2 H₁₁₂ OD. Ho H1 H2 The test statistic, t, is (Round to two decimal places as needed.)