# Standardized Test Statistic

1. Find the standardized test statistic to test the claim that mean1 = mean 2. Two samples are randomly selected from each population. The sample statistics are given below.

n1 = 50 n2 = 6

x1 = 31 x2 = 29

s1 = 1.5 s2 = 1.9

x has a line above it

2. In a recent survey in gun control laws, a random sample of 1000 women showed that 65% were in favor of stricter gun control laws. 1000 men at 60%. Construct a 95% confidence interval for p1 - p2.

3. Data sets are dependent find d

A 37 35 54 50 38

B 35 31 32 42 29

4. Find the standardized test statistic to test the claim the mean 1 < mean 2. Two samples are randomly selected from each population. The sample statistics are given below.

n1 = 35 n2 = 42

x1 = 22.649997 x2 = 25.2000008

s1 = 2.9 s2 = 2.8

x has a line over it

5. Find the standardized test statistic, z, to test the claim that p1 is not equal to p2. The sample statistics listed below are from independent samples.

Sample statistics. n1 = 1000, x1 = 250, and n2 = 1200, x2 = 195.

#### Solution Preview

1. Find the standardized test statistic to test the claim that mean1 = mean 2. Two samples are randomly selected from each population. The sample statistics are given below.

n1 = 50 n2 = 6

x1 = 31 x2 = 29

s1 = 1.5 s2 = 1.9

x has a line above it

Since one sample has less than 30 data points, first calculate the pooled estimate of standard deviation.

sp=[((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2)]^0.5

sp=((49*1.5^2+5*1.9*^2)/(50+6-2))^0.5=1.5471

Then calculate the standard error = sp*(1/n1+1/n2)^0.5 = 1.5471*(1/50+1/6)^0.5=0.6684

Standardized test statistic = (x1-x2)/standard error = (31-29)/0.6684=2.99

Since the test statistic is 2.99, we are most likely to reject the null depending upon ...

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