A random sample of 25 women resulted in systolic blood pressure levels with a mean of 142 and a standard deviation of 6.9. A random sample of 61 men resulted in systolic blood pressure levels with a mean of 92 and a standard deviation of 2. Use a 0.025 significance level and the p-value method to test the claim that blood pressure levels for women vary more than blood pressure levels for men. Enter the smallest critical value. (Round your answer to nearest ten-thousandth.)

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A random sample of 25 women resulted in systolic blood pressure levels with a mean of 142 and a standard deviation of 6.9. A random sample of 61 men resulted in systolic blood pressure levels with a mean of 92 and a standard deviation of 2. Use a 0.025 significance level and the p-value method to test the claim that blood pressure levels for women vary more than blood pressure levels for men.

Enter the smallest critical value. (Round your answer to nearest ten-thousandth.)

Expert Solution
Step 1

Given:

The sample size of the women resulted in systolic blood pressure levels is n1=25.

The sample size of the men resulted in systolic blood pressure levels is n2=61.

The sample mean of the women resulted in systolic blood pressure levels is x¯1=142.

The sample mean of the men resulted in systolic blood pressure levels x¯2=92.

The sample standard deviation of the women resulted in systolic blood pressure levels s1=6.9.

The sample standard deviation of the men resulted in systolic blood pressure levels s2=2.

The level of significance is α=0.025.

The researcher claims that the blood pressure levels for women vary more than blood pressure levels for men. So the statistical hypothesis formed is:

H0: μ1μ2

H1: μ1>μ2

where μ1 and μ2  are the true representative of the population mean of blood pressure levels for women and men.

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