Question

If I calculate a z test statistic of 4.84, and my α=0.05, what decision should I make about the hypothesis? (Calculate the p-value for a 2-sided test to make your decision.)

Fail to reject the null hypothesis that the proportion of American adults who voted for Obama in 2008 was 0.55.

Reject the null hypothesis that the proportion of American adults who voted for Obama in 2008 was 0.55.

Reject the alternative hypothesis that the proportion of American adults who voted for Obama in 2008 was not equal to 0.55.

Fail to reject the alternative hypothesis that the proportion of American adults who voted for Obama in 2008 was not equal to 0.55.

Answer 1

Solution:

Given:

z test statistic = 4.84,

Level of significance = α = 0.05.

We have to calculate the p-value for a 2-sided test to make decision.

For two tailed test , p-value is:

p-value = 2* P(Z > z test statistic) if z is positive

p-value = 2* P(Z < z test statistic) if z is negative

Since z is positive, we use:

p-value = 2* P(Z > z test statistic)

p-value = 2* P(Z > 4.84)

Since z = 4.84 is not listed z table, we use TI 84 plus calculator or Excel command:

Using TI 84 :

Press 2ND and VARS

select normalcdf(

Enter numbers:

Since we have to find:

P( Z> 4.84) ,lower limit would be 4.84 and upper limit would be inifinity, so we enter very large number 9999999

Click on paste and press Enter two times.

Thus we get:

P( Z > 4.84) = 6.5007E-7

Since this is scientific number with negative power 7, we need to move 7 decimal places to left side.

thus

P( Z > 4.84) = 6.5007E-7

P( Z > 4.84) = 0.00000065007

P( Z > 4.84) = 0.00000065

thus

p-value = 2* P(Z > 4.84)

p-value = 2* 0.00000065

p-value = 0.00000130

Decision Rule:
Reject null hypothesis H0, if p-value < 0.05 level of significance, otherwise we fail to reject H0

Since p-value = 0.000000130 < 0.05 level of significance, we reject null hypothesis H0.

Thus correct answer is:

Reject the null hypothesis that the proportion of American adults who voted for Obama in 2008 was 0.55.

We can use following Excel command:

p-value = 2* P(Z > 4.84)

p-value = 2* (1- P(Z < 4.84) )

Thus excel command is:

=2*(1-NORM.S.DIST(4.84,TRUE))

= 0.00000130