A genetic experiment involving peas yielded one sample of offspring consisting of 423423 green peas and 145145 yellow peas. Use a 0.050.05 significance level to test the claim that under the same​ circumstances, 2525​% of offspring peas will be yellow. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution.

A company claims that their new product has an average lifespan of at least 5 years. A sample of 25 products is randomly selected, and the mean lifespan is found to be 4.6 years with a standard deviation of 0.8 years. Conduct a hypothesis test at the 1% significance level to determine whether there is sufficient evidence to reject the company's claim.

Bone mineral density (BMD) is a measure of bone strength. Studies show that BMD declines after age 45. The impact of exercise may increase BMD. A random sample of 59 women between the ages of 41 and 45 with no major health problems were studied. The women were classified into one of two groups based upon their level of exercise activity: walking women and sedentary women. The 39 women who walked regularly had a mean BMD of 5.96 with a standard deviation of 1.22. The 20 women who are sedentary had a mean BMD of 4.41 with a standard deviation of 1.02. Which of the following inference procedures could be used to estimate the difference in the mean BMD for these two types of women

A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of dress is designed to be 29 inches. The company regularly tests the lengths of the garments to ensure quality control, and if the mean length is found to be significantly longer or shorter than 29 inches, the machines must be adjusted. The most recent simple random sample of 18 dresses had a mean length of 33.46 inches with a standard deviation of 5.89 inches. Assume that the population distribution is approximately normal. Perform a hypothesis test on the accuracy of the machines at the 0.025 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision. Answer 田 Tables 回 Keypad Keyboard Shortcuts We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the mean length of the particular size of dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.…

In tests of a computer component, it is found that the mean time between failures is  909  hours. A modification is made which is supposed to increase reliability by increasing the time between failures. Tests on a sample of  25  modified components produce a mean time between failures of  955  hours. Using a  1%  level of significance, perform a hypothesis test to determine whether the mean time between failures for the modified components is greater than  909  hours. Assume that the population standard deviation is  53  hours.

Is the strep virus getting harder or easier to heal? Pediatricians are interested in studying the average length of time patients with strep are running fever while on antibiotics. In previous years, the average length of time patients ran fever with strep while on antibiotics was 1.8 days. A random sample of forty-six patients with strep ran fever while on antibiotics for an average of 2.3 days with standard deviation 1.2. at the 5% significance level, can pediatricians conclude that the average amount of time patients with strep run fever while on antibiotics has changed? Assume the random variable has a normal distribution.   a. Find the rejection region b. Find the p-value c. State the Decision and the Conclusion in terms of the problem d. If Ho is rejected, find and interpret the appropriate confidence interval.

A randomized controlled trial is run to evaluate the effectiveness of a new drug for asthma in children. A total of 250 children are randomized to either the new drug or a placebo (125 per group). The mean age of children assigned to the new drug is 12.4 with a standard deviation of 3.6 years. The mean age of children assigned to the placebo is 13.0 with a standard deviation of 4.0 years. Suppose that there are 63 boys assigned to the new drug group and 58 boys assigned to the placebo group. Is there a statistically significant difference in the proportions of boys assigned to the treatments? Run the appropriate test at a 5% level of significance.