Discuss the below:
Q1) The distribution of sample mean for samples of 500 homes is normal with a mean of 2.64 and a standard deviation of 0.06. Suppose you select a random sample of n=500 homes and determine that the mean number of people per home for this sample id 2.55. How many standard deviations is the sample mean of the sampling distribution? What is the probability that a second sample would be selected with a mean less than 2.55?
Q2) You have 42% of a company are woman, you also know the normal mean is at .42 and a standard deviation of 0.21. Suppose you take a random sample of employees and find that the proportion of women is 0.45. How many standard deviations is the sample mean of the sampling distribution? What is the probability that a second sample would be selected with a proportion greater than 0.45?
Q3) Telephones: A random sample of n=31 homes is asked the number of telephones in a home: data as follows;
1 0 2 3 2 3 4 2 1 1 2
4 3 2 3 3 0 1 0 1 3 2
4 3 2 1 4 0 1 2 3
a) What's the mean # of telephones for the sample?
b) What is the standard deviation?
c) Whats the 95% confidence interval for the estimate?
d) Whats the best estimate for the mean number of telephones of all homes?