A manufacturer of electric batteries claims that the average capacity of a certain type of battery that the company produces is at least 140 ampere-hours with a standard deviation of 2.66 ampere-hours. An independent sample of 20 batteries gave a mean of 138.47 ampere-hours. Test at 5 percent significance level the null hypothesis that the mean life is 140 ampere-hours against alternative that it is lower. Can the manufacturer's claim be sustained on the basis of this sample?

The mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same? (Assume a 5% level of significance.)

The Edison Electric Institute has published figures on the annual number of kilowatt hours expended by various home appliances. It is claimed that a vacuum cleaner expends an average of 46 kilowatt hours per year. A random sample of 12 homes included in a planned study indicates that vacuum cleaners expend an average of 42 kilowatt hours per year with a standard deviation of 11.0 kilowatt hours. This sample data is to be tested with the goal of showing that the vacuum cleaners expend on average less than 46 kilowatt hours annually. Test at the 0.05 level of significance. a. To test the hypothesis, his null and alternative hypotheses are: Ho: and H1: b. What is the appropriate decision parameter at the 95% level of confidence? (“the null will be rejected if the z- or t- value is...). c. Determine the sample statistic using the sample data above. d. Based on his hypothesis test, should the null hypothesis be rejected? Explain why or why not. е. Obtain the confidence interval, at the 95%…

The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $14,124. The following year, a random sample of 20 two-year institutions had a mean of $17,124 and a standard deviation of $3700. Is there sufficient evidence at the alpha level of 0.05 to conclude that the mean cost has increased.  Show 6 steps of hypothesis

Does chronic hepatitis C infection impact bone mineral density? In the general population of healthy young adults, bone mineral density is Normally distributed, and density scores are standardized to have a mean u of 0 and a standard deviation o of 1. A study examined the bone densities of a random sample of 28 adult men suffering from chronic hepatitis C infection. Their mean standardized bone density was -0.61. Does this provide strong evidence that the mean standardized bone density of adult men suffering from chronic hepatitis C infection is less than 0?

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.

Suppose an investigator is looking at age at menarche (first period) and its relationship to the onset of breast cancer in women. The investigator conducted a thorough literature review and wanted to test out the hypothesis that women with an earlier menarche are less likely to develop breast cancer. Suppose the investigator conducted a population based study and found that the average age at menarche was 12.3 years with a standard deviation of 1.3 years. Assuming the investigator finds that women in the highest 10% of the distribution have a relative risk of 1.4 for developing breast cancer. What age at menarche correlates to this percentile? (Hint: highest 10% means 90th percentile)