The weights of men in a particular age group have mean ? = 176 pounds and standard deviation ? = 36 pounds. (a) For randomly selected samples of n = 36 men, what is the standard deviation, s.d., of the sampling distribution of possible sample means? s.d.(x) =  (b) For randomly selected samples of n = 144 men, what is the standard deviation, s.d., of the sampling distribution of possible sample means? s.d.(x)  =  (c) In general, how does increasing the sample size affect the standard deviation of the sampling distribution of possible sample means? Parts (a) and (b) provide a hint. Increasing the sample size      the value of the standard deviation of the sampling distribution of the sample mean. A fourfold increase in sample size multiplies the standard deviation by a factor of        .

(Q5). The data on monthly rents, in dollars, for independent random samples of newly completed apartments in three U.S. regions are presented in the table below.  Assume that the population standard deviation of the monthly rents in the three regions are equal and the populations are normally distributed.   Northeast                   South              _____West       1005                              891                            1025         898                              630                            1012         948                              861                            1090       1181                                                                  926 _______________________________   (a). Do the data indicate that there is a difference in the monthly rent for the three regions?  Discuss the assumptions you have made to carry out your analysis. Use a significance level of 10%.                                                           (b). Interpret your conclusion in…

The following table shows the number of people that have either 0, 1, 2 or 3 cars registered in their name, from a sample of 311 people. x n 0 93 1 91 2 60 3 67 (a) Find the mean number of cars owned for this sample. Give your answer to at least 2 decimal places. (b) Find the standard deviation of cars owned for this sample. Give your answer to at least 2 decimal places.

When asked: "What is the distribution of X ? X ~ N(___,___)." This notation is referring to N, a normal distribution, with the mean given in the first space and the standard deviation in the second space. Remember that the standard deviation of the sample means is different from the population standard deviation. The lengths of adult males' hands are normally distributed with mean 190 mm and standard deviation 7 mm. Suppose that 11 individuals are randomly chosen. Round final answers to 4 decimal places. a. What is the distribution of x? x N( b. For the group of 11, find the probability that the average hand length is more than 189. c. Find the first quartile for the average adult male hand length for this sample size. d. For part b), is the assumption that the distribution is normal necessary? Yes No

Use z scores to compare the given values. The tallest living man at one time had a height of 238 cm. The shortest living man at that time had a height of 142.4 cm. Heights of men at that time had a mean of 175.45 cm and a standard deviation of 5.59 cm. Which of these two men had the height that was more extreme? ... Since the z score for the tallest man is z = 0 and the z score for the shortest man is z = the man had the height that was Im- more extreme. (Round to two decimal places.) shortest tallest

Suppose x has a normal distribution with mean ? = 53 and standard deviation ? = 7.Describe the distribution of x values for sample size n = 4. (Round ?x to two decimal places.) ?x =  ?x =  Describe the distribution of x values for sample size n = 16. (Round ?x to two decimal places.) ?x =  ?x =  Describe the distribution of x values for sample size n = 100. (Round ?x to two decimal places.) ?x =  ?x =

The distribution of the number of motor vehicles per household in the United States (the population) and sampling distributions of the mean for samples of size 4 and 10 are shown in below. A.Which distribution is which? Make a rough estimate of the mean and standard deviation of each distribution. Explain the reasons of your choices.b. The mean of the population is about 1.7. Theoretically, what is the mean of the sampling distribution for samples of size 4? Of size 10? Are these computed means consistent with your estimates of the means in the histograms? Briefly explain.c. The standard deviation of the population is about 1. Theoretically, what is the Standard Error (SE) of the sampling distribution for samples of size 4? Of size 10? Are these computed SEs consistent with your estimates of the SEs in the histograms? Briefly explain.d. Compare the shapes of the three distributions. Are the shapes consistent with the Central Limit Theorem? Briefly explain.

Can someone explain the formulas used in these type of questions and where each number belongs in the formula     The average size of a farm in Texas is 185 acres. The average size of a farm in Kansas is 220 acres. Assume that the data were obtained from two samples with standard deviations of 40 and 15 acres, respectively, and a sample size of 10 and 12, respectively. Can it be concluded with a=0.05 that the average size of the farms in the two states is different? Assume that the population is normally distributed.