11. Suppose the average lifetime of a certain type of car battery is known to be 60 months. Consider conducting a two-sided test on it based on a sample of size 25 from a normal distribution with a population standard deviation of 4 months. a) If the true average lifetime is 62 months and a =0.01, what is the probability of a type II error?   b) What is the required sample size to satisfy the type II error probability of b(62) = 0.1?

Please do the following questions with full handwritten working out. Mean= 0.177911 Variance=0.057632

Please note the question is: What is the distribution of the t-test statistic if m, n -----> ∞ ?

The University of Florida is interested in determining if there is a difference in the amount of money spent on food every two weeks between male and female students. They take a random sample of 20 male students (group 2) and 20 female students (group 1). They also find that xbar2 is 106 with a standard deviation of 14, and xbar1 is 146 with a standard deviation of 39. Do not assume equal variances. Find the test statistic for the difference in the amount of money spent. (Round your answer to one number after the decimal.)

Solve by showing steps properly

If x represents a random variable with mean 137 and standard deviation 16, then the standard deviation of the sampling distribution of the means with sample size 64 is 2. True O False

Suppose that average rainfall in your city is normally distributed, and for the past 36 months, the rainfall has been 0.5 inches per day on average with a standard deviation of 0.16. Let x be a random variable that has a normal distribution and represents the rainfall in inches per day. Using a 0.05 level of significance, you want to test the hypothesis that monthly rainfall has been 0.7 inches per day on average. What conclusion do you make from your test? Select one: a. Reject H0; the average rainfall is not 0.5 inches. b. Reject H0; the average rainfall is not 0.7 inches. c. Do not reject H0; the average rainfall is still 0.5 inches. d. Do not reject H0; the average rainfall is still 0.7 inches.

In the manufacture of steel rollers to fit an assembly, the external diameter is considered to be a random variable with mean equal to 23 mm and variance equal to 0.0036 cm2. 1.5 is supported standard deviations more than the mean and 3.5 standard deviations below average. A piece with a diameter below such specifications is considered waste, whereas a piece with a diameter larger than specified must be reprocessed. Which is the percentage of pieces that:to. They are being wasted.b. They need to be reprocessed.c. Acceptable.d. If you want to establish that the reprocessing is 5% of the rollers and waste of 1%, than specification limit would recommend.

The weight of a male bald eagle has approximately a normal distribution with mean ?= 7.4 pounds and a standard deviation of ?= 1.6 pounds. Suppose we take a random sample of n=64 male bald eagles. Let X̄ be the random variable representing the mean weight in pounds of the 64 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 84 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 64 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 64 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X̄ (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the…