Download 7.19 Random samples of size n were selected from populations with

7.19 Random samples of size n were selected from populations with the means and variances
given here. Find the mean and standard deviation of the sampling distribution of the sample
mean in each case:
a.
n = 36 , μ = 10 , σ2 = 9
b.
n = 100 , μ = 5 , σ2 = 4
c.
n = 8 , μ = 120 , σ2 = 1
7.20 Refer to Exercise 7.19.
a.
If the sampled populations are normal, what is the sampling distribution of x̅ for parts a,
b, and c?
b.
According to the Central Limit Theorem, if the sampled populations are not normal, what
can be said about the sampling distribution of x̅ for parts a, b, and c?
7.28 Tomatoes Explain why the weight of a package of one dozen tomatoes should be
approximately normally distributed if the dozen tomatoes represent a random sample.
7.40 Random samples of size n = 500 were selected from a binomial population with p=.1.
a.
Is it appropriate to use the normal distribution to approximate the sampling distribution
of p̂? Check to make sure the necessary conditions are met.
Using the results of part a, find these probabilities:
b.
p̂ > .12
c.
p̂ < .10
d.
p̂ lies within .02 of p
7.60 A finite population consists of four elements: 6, 1, 3, 2.
a.
How many different samples of size n=2 can be selected from this population if you
sample without replacement? (Sampling is said to be without replacement if an element
cannot be selected twice for the same sample.)
b.
List the possible samples of size n=2.
c.
Compute the sample mean for each of the samples given in part b.
d.
Find the sampling distribution of x̅. Use a probability histogram to graph the sampling
distribution of x̅.
e.
If all four population values are equally likely, calculate the value of the population mean
μ. Do any of the samples listed in part b produce a value of x̅ exactly equal to μ?
7.61 Refer to Exercise 7.60. Find the sampling distribution for x̅ if random samples of size n=3 are
selected without replacement. Graph the sampling distribution of x̅.