A random sample of 850 high school girls showed that 400 ha

. A random sample of 850 high school girls showed that 400 had done strenuous exercise over the past year. The researcher wants to test the hypotheses below for p= the proportion of all high school girls who do strenuous exercise

H₀: p = 0.50

H_a: p < 0.50

Use a=.05.

Use traditional and p value approach

Solution

Sample proportion = 400/850 = 0.470588

Hypothetical proportion = 0.50

Std error = 0.5/rt 850 = 0.01715

H0: P sample proportion = 0.50

Ha: p <0.50

Left tailed test

Alpha = 0.05

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p difference = -0.02941

Test statistic = -1.72

p value = 0.0427

As p <alpha

reject null hypothesis.

p < 0.50 is statistically evident.