anufacturer claims that the mean lifetime, μ, of its light bulbs is 54 months. The standard deviation of these lifetimes is 6 months. Forty-six bulbs are selected at random, and their mean lifetime is found to be 55 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 54 months? State the null hypothesis  H0  and the alternative hypothesis  H1

Researchers conducted a study to determine whether magnets are effective in treating back pain.  The results are shown in the table for the treatment (with magnets) group and the sham or (placebo) group.  The results are a measurement of the reduction in back pain.  Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviation are equal. M1 (treatment )                                       M2( sham) n=29                                                        n=20 x bar=0.55                                             x bar=0.39 s= 0.84                                                  s=1.31   a.) us a 0.05 signfigance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment 1. Write a null hypothesis and alternative hypothesis 2. What is the test statistic? 3. What is the P-Value? 4. State the conclusion to…

A random sample of size 16 from a normal distribution has standard Leviation s =74. Test H: 0=32 Versus H : o>32. Use the a=0.01 level of significance.

To evaluate the effect of a treatment, a sample is obtained from a population with a mean of m = 20, andthe treatment is administered to the individuals in thesample. After treatment, the sample mean is found tobe M = 21.3 with a variance of s2= 9.a. Assuming that the sample consists of n = 16individuals, use a two-tailed hypothesis test witha = .05 to determine whether the treatment effectis significant and compute both Cohen’s d and r2to measure effect size. Are the data sufficient toconclude that the treatment has a significant effectusing a two-tailed test with a =.05?b. Assuming that the sample consists of n = 36 individuals, repeat the test and compute both measuresof effect size.c. Comparing your answers for parts a and b, howdoes the size of the sample influence the outcomeof a hypothesis test and measures of effect size?