Question

You want to estimate the proportion of American voters who are optimistic about the state of the economy. How large a sample would be needed to ensure a 95% confidence level that the actual population proportion of American voters will be no more than 3 percentage points from the sample proportion?(hint, no information about ? ^)

(a) 1506

(b) 1068

(c) 3152

(d) 938

Suppose at the 90% confidence level we calculate a confidence interval described by 23.8<?<26.2. Which of the following statement can not be made about this result?

(a) The sample mean was 25.

(b) The population mean is 25.

(c) The margin of error is 1.2

(d) We are 90% confident that the population mean is in the interval (23.8,26.2)

Suppose you were to take samples of size 64 from a population with a mean of 12 and a standard deviation of 3.2. What would be the standard deviation of the sampling distribution of sample means?

(a) 0.60

(b) 0.20

(c) 0.40

(d) 0.30

In hypothesis testing the significance level ? represents:

(a) A Type I error.

(b) A Type II error.

(c) Rejecting the null hypothesis when it is false

(d) Rejecting the alternative hypothesis when it is false.

Answer 1

Question 1

p̂ = 0.5
q̂ = 1 - p̂ = 0.5
Critical value Z(α/2) = Z(0.05/2) = 1.96
n = ( Z(α/2)2 * p̂ * q̂ )/e2
n = ( Z(0.05)2 * 0.5 * 0.5)/ 0.032
n = 1068

Question 2

90% confidence interval is  23.8<?<26.2

Margin of error = ( 26.2 - 23.8 ) / 2 = 1.2

Sample mean = ( 26.2 + 23.8 ) / 2 = 25

Interpretation of confidence interval is   We are 90% confident that the population mean is in the interval (23.8,26.2)

statement can not be made about this result

(b) The population mean is 25.

Question 3

standard deviation of the sampling distribution of sample means

σX̅ = σ / √ (n) = 3.2/√64 = 0.4

Question 4

In hypothesis testing

Type I error = α = P ( Reject H0 | H0 is true )

Type II error = ß = P ( Accept H0 | H0 is false )

Here, α is level of significanc is type I error.