A consumer products company is formulating a new shampoo and interested in studying the mean foam height (in mm). Assume the foam height approximately follows a normal distribution with known variance of  σ2 = 400 mm2. A random sample of 9 such new shampoos results in a mean foam height 165 mm. Test if there is sufficient evidence to support the claim that the mean foam height of the new shampoo is different from 160.5 mm at α = 0.05. Which of the following statements is INCORRECT?

The heights of a particular breed of horse are normally distributed with a standard deviation of 6.5cm. The mean is unknown but is somewhere between 140cm and 150cm. Which one of the following statements cannot be true?Group of answer choicesThe median of the distribution is 148cmA large horse of this breed could plausibly reach a height of 163cmAbout 5% of horses of this breed have heights outside the range 130cm to 156cm.About 5% of horses of this breed have heights outside the range 142cm to 155cm.

17.  In a modeling agency, a researcher wishes to see if the average height of female models is less than 67 inches, as the coach claims. A random sample of 60 models has an average height of 65.8 inches. The standard deviation of the sample is 1.7 inches. At 𝛼 = 0.05, which of the following shows the appropriate rejection of the given problem?*A.B.C.D.

An investigator wants to assess whether the mean (mu) = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 25 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed. Which of the following is an appropriate conclusion (alpha= .05)? Group of answer choicesnull hypothesis should be revisedthe average total weight of all passengers appears to be not greater than 185 pounds.the average total weight of all passengers appears to be greater than 185 pounds.

Suppose the lifetime (in hours) of a battery brand is normally distributed. A random sample of 19 batteries results in a sample variance 4.75 hours2. We want to test if there is significant/sufficient evidence in the data to claim that the variance of the battery life population is different than 8 hours2 at 𝛼=0.1, which of the following is INCORRECT?

An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally with the mean μ = 10 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.Below is the output:Which of the following represents the correct conclusion we can make based on the output (and at the usual significance level of 0.05)? The data provide enough evidence to reject H0 and to conclude that the mean volume per cup is lower than the target level of 10 oz. The data provide enough evidence to accept H0 and to conclude that the mean volume per cup is at the target level of 10 oz. The data do not provide enough evidence to reject H0, so we accept it, and conclude that the mean volume per cup is at the target level of 10 oz. The data do not provide enough evidence to reject H0, nor to conclude that the mean volume per cup is lower than the target level of 10 oz.Question 4