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# Z-tests and Linear Regression

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Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > c) = 0.0643, find c.

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(-b < z < b) = 0.8664, find b.

In a Gallop poll of 1012 randomly selected adults, 9% said that cloning of humans should be allowed. Use a 0.05 significance level to test the claim that less than 10% of all adults say that cloning of humans should be allowed. Accept or reject the Null Hypothesis?

In previous tests, baseballs were dropped 24 feet onto a concrete surface, and they bounced an average of 92.84 inches. In a test sample of 40 new balls, the bounce heights had a mean of 92.67 inches and a standard deviation of 1.79 inches. Use a 0.05 significance level to determine whether there is sufficient evidence to support the claim that the new balls have bounce heights with a mean different from 92.84 inches. Accept or reject the null hypothesis?

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n1 = 10,239 n2 = 9,877
x1 = 101 x2 = 56
Assume that you plan to use a level of significance of a= .05 test to claim that p1=p2. Use the given samples sizes and numbers of successes to find the critical values of the z statistic.

Assume that you plan to use a level of significance of a= .05 test to claim that p1=p2. Use the given samples sizes and numbers of successes to find the pooled estimate of p.

Given the following data:
Height (in.) 71 70.5 71 72 70 70 66.5 70 71
Weight (lbs.) 125 119 128 128 119 127 105 123 115
Find the value of the y-intercept of the linear regression equation. Find the equation of the linear regression equation.

Using data collected from the FBI and the Bureau of Alcohol, Tobacco, and Firearms, the number of registered automatic weapons and murder rate was obtained for each of eight randomly selected states. The value of the linear correlation coefficient is r = 0.885. Find the critical value (a = .05) of the linear correlation coefficient.

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#### Solution Preview

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > c) = 0.0643, find c.

1.23

1.50

1.52

-2.42
To find this, look at a z-distribution table. Find the value of z such that the area to the right of z is 0.0643 (or the area between 0 and z is 0.4357). The answer is z = 1.52.
Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(-b < z < b) = 0.8664, find b.

1.23

1.50

1.52

-2.42
This is similar to the previous question. Find the value of z such that the area between 0 and z is 0.8664/2 = 0.4332. The answer is z = 1.50.
In a Gallop poll of 1012 randomly selected adults, 9% said that cloning of humans should be allowed. Use a 0.05 significance level to test the claim that less than 10% of all adults say that cloning of humans should be allowed. Accept or reject the Null Hypothesis?

Accept.

Reject.
The formula for the z-statistic in this case is:

z = (0.09 - 0.10) / &#8730;(0.10)(1 - 0.10)/1012 = -0.01 / &#8730;0.00009 = -1.06
The p-values associated with this z-value is p = 0.14. You cannot reject the null hypothesis at the 0.05 level.