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A poll of city residents found that 50% of likely voters support a ballot regard

ID: 3232854 • Letter: A

Question

A poll of city residents found that 50% of likely voters support a ballot regarding restrictions on stem cell research. A professor claims this percentage is higher for students at his university. If 61 out of 100 randomly selected students at his university support restrictions on stem cell research test the professors claim using a 5% significance level.

a. Write the hypotheses and identify the direction of the test.

b. Identify the given values with their correct symbol and find the test value.

c. Complete the hypothesis test using the p-value method.

The test value is =

The P value is =

The p value is ____ than the significance level a.

The decision is _________ the null hypothesis.

Explanation / Answer

This is a test of proportions

now P = 0.5 and p = 61/100 = 0.61 , n = 100

a)

Hypothesis is

H0 : 50% of likely voters support a ballot regarding restrictions on stem cell research

H1 : More than 50% of likely voters support a ballot regarding restrictions on stem cell research

b) H0 P = 50%

H1 P > 50% , it is a directional test with "greater" symbol

c)

The hypothesis test is

The test statistic is a z-score (z) defined by the following equation.

z = (p - P) /

Compute the standard deviation () of the sampling distribution.

= sqrt[ P * ( 1 - P ) / n ]

so sigma is sqrt(0.5*0.5/100) = 0.05

and Z = (0.61-0.5)/0.05 = 2.2

now we check the p value as

P(Z>2.2)

P ( Z>2.2 )=1P ( Z<2.2 )=10.9861=0.0139 , please keep the z tables handy for the p value calculation

as the p value is less than 0.05 (our level of signficance) , we reject the null hypothesis in favor of alternate hypothesis and conclude that

More than 50% of likely voters support a ballot regarding restrictions on stem cell research