Question

Problem (12 points) Test at 0.05 significance level the claim in a college catalog that the mean price of a textbook at the college bookstore is less than 575. Assume that the prices of textbooks are normally distributed From a random sample of 16 textbooks, a mean of $70.41 with a standard deviation of $19.70, were obtained Problem #2 (12 points) A sample of 54 bears from Yellowstone National Park produces a mean weight of 182.91b. Assuming that is known and equal to 121.8 lb, use a 0.10 significance level to test the claim that the population mean weight of all such bears is less than 200 lb. Problem 13 (12 points) A random sample of 25 two-month-old babies from a hospital is obtained, and the mean head circumference is found to be 40.6 cm. with a standard deviation of 1.6cm. Under the assumption that we are sampling from a population that is essentially normal. Test the claim that the mean bead circumference of all two-month-old babies is equal to 40.0cm. (use a significance level of a -0.05) Problem #4 (5 points) A media research company wants to estimate the mean amount of time (in minutes) that college students spend watching TV each weckday. Find the sample size necessary to estimate that mean with a 15minute margin of error. Assume that a 96% confidence level is desired and that a pilot study showed that the standard deviation is estimated to be 112.2 minutes. Problem #5 (8 points) The mean weight of 12 randomly selected newly born babies from a local hospital was found to be 7.25lbs and the standard deviation was found to be 0.92lbs. Assume that weights of newly born babies are normally distributed a) Find a 90% confidence interval for the average weight of newly born babies b) Find a 95% confidence interval for the average weight of newly born babies
#2 please

Answer 1

2. Here claim is that mean is less than 200

So hypothesis here is
Ho :μ = 200
vs
H, :μ< 200

As population standard deviation is known we will use z statistics

- и 182.9 – 200 121 .8 — = -1.03

P value is

Plz < -1.03) = 0.1515 > a=0.10

As P value is greater than alpha we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean is less than 200.