**Need help with these 5 questions (multiple choice)! Thank you in advance.

1) Based on a sample of size 200, you estimate the mean of a population to be 135.You know from past research that the population standard deviation is 10.What is the 95% confidence interval for the true value of the mean?

Group of answer choices

133.6 to 136.4

131.6 to 138.4

120 to 150

135 to 160

2) Based on a sample of size 150, you estimate a proportion to be .45.What is the 95% confidence interval for the true proportions?

Group of answer choices

.37 to .53

.44 to .46

.27 to .63

.47 to .57

3) Suppose we have an existing confidence interval for a population mean.If we increase the sample size by a factor of 100, what happens to the width of the confidence interval?

Group of answer choices

It remains the same.

It decreases by a factor of 100.

It increases by a factor of 10.

It decreases by a factor of 10.

4) What is the relationship between the width of the confidence interval and the margin of error?

Group of answer choices

They are unrelated concepts.

They are identical.

The margin of error is twice the length of the confidence interval.

The length of the confidence interval is twice the margin of error.

5) Identifyallof the correct statements.

Group of answer choices

The disribution of estimates of a proportion is always normal.

The standard error of the sampling distribution of a proportion is directly proportional to the square root of the sample size.

If the product of the sample size and the population proportion is greater than 10, we can assume that the sampling distribution of the proportion is normal.

If we increase the sample size used in estimating a proportion by a factor of 4, we will decrease the standard error of the sampling distribution by a factor of 2.