The life in hours of a battery is known to be approximately normally distributed, with standard deviation 6 = 1.25 hours. A random sample of 10 batteries has a mean life of = 40.5 hours. (a) Is there evidence to support the claim that battery life exceeds 40 hours? Use a = 0.050. The battery life significantly different greater than 40 hours at a = 0.050. (b) What is the P-value for the test in part (a)? P-value = i Round your answer to three decimal places (e.g. 98.765). (c) What is the B-error for the test in part (a) if the true mean life is 42 hours? B = i Round your answer to five decimal places (e.g. 98.76543). (d) What sample size would be required to ensure that does not exceed 0.1 if the true mean life is 44 hours? i batteries

The heights of adult females are approximately normally distributed, with an estimated mean of 65.0 inches and an estimated standard deviation of 3.00. Some researchers hypothesized that the actual standard deviation, o, of heights of adult females is greater than 3.00. These researchers chose a random sample of 20 adult females. The mean height of this sample was 64.9 inches, and the standard deviation was 3.44. Is there enough evidence to conclude, at the 0.1 level of significance, that the standard deviation of adult female heights is greater than 3.00? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H1. p Ho :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c) Find the value of the test statistic. (Round to three or more…

A survey of 46 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated.You're testing the claim that the mean difference is greater than 1.3.From the sample, the mean difference was 1.55, with a standard deviation of 0.6.Calculate the test statistic, rounded to two decimal places

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 62 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 58 and 62?ans =  %

Recent study stated that if a person chewed gum, the average number of sticks of gum he or she chewed daily was 8. To test the claim, a researcher selected a random sample of 36 gum chewers and found the mean number of sticks of gum chewed per day was 9. The standard deviation of the population is 1. a- At a = 0.05, is the number of sticks of gum a person chews per day actually greater than 8? Calculate the value of the test statistic and state the hypotheses, and conclusion. b- Find a 95% confidence interval for the average number of sticks of gum he or she chewed daily c- Explain what does “a 95% confidence” means.