Question

In testing the hypothesis H₀:  μ = 800 vs. H_a:  μ ≠ 800. A sample of size 40 is chosen. the sample mean was found to be 812.5 with a standard deviation of 25, then the of the test statistic is:

		Z=0.0401
		Z=-3.16
		Z=3.16
		Z=12.5

In a sample of 500 voters, 400 indicated they favor the incumbent governor.  The 95% confidence

interval of voters not favoring the incumbent is

		0.782 to 0.818
		0.120 to 0.280
		0.765 to 0.835
		0.165 to 0.235

A Type II error is committed if we make:

		a correct decision when the null hypothesis is false
		correct decision when the null hypothesis is true
		incorrect decision when the null hypothesis is false
		incorrect decision when the null hypothesis is true

What is the value of z _α/2 for an 85% confidence interval?

		1.44
		.385
		.0279
		.19

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

		77.769
		72.231
		72.727
		77.273

Answer 1

Here we have to test that

where

n = sample size = 40

Sample mean =

Sample standard deviation = s = 25

Here population standard deviation is not known but sample size n is large, n = 40 > 30

So we use z test.

Test statistic:

z = 3.16 (Round to 2 decimal)

Test statistic = z = 3.16

n = number of voters selected randomly = 500

x = number of voters not favor the incumbent governor = 500 - 400 = 100

Sample proportion:

= proportion of voters not favoring the incumbent = 0.2

95% Confidence interval of voters not favoring the incumbent is

where zc is z critical value for (1+c)/2 = (1+0.95)/2 = 0.975

zc = 1.96 (From statistucal table of z values)

0.165 < p < 0.235

95% Confidence interval of voters not favoring the incumbent is (0.165, 0.235)

A Type II error is committed if we make:

incorrect decision when the null hypothesis is false.

Confidence level = c = 0.85

alpha = 1 - c = 1 - 0.85 = 0.15

alpha/2 = 0.15/2 = 0.075

z for 0.075 is z = -1.44

z for (1-0.075) = 0.925 is z = 1.44