Question

A poll showed the approval rating to be 0.49 ​(49​%).

A second poll based on 2000 randomly selected voters showed that 964 approved of the job the president was doing. Do the results of the second poll indicate that the proportion of voters who approve of the job the president is doing is significantly lower than the original​ level? Explain. Assume the a=0.01 level of significance.

Find the test statistic for this hypothesis test.

z=_________

​(Round to two decimal places as​ needed.)

Answer 1

SOLUTION:

From given data,

A poll showed the approval rating to be 0.49 ​(49​%).

A second poll based on 2000 randomly selected voters showed that 964 approved of the job the president was doing. Do the results of the second poll indicate that the proportion of voters who approve of the job the president is doing is significantly lower than the original​ level? Explain. Assume the = 0.01 level of significance.

Where,

Claimed proportion = p = 0.49

n = 2000

x = 964

Sample proportion = = x/n = 964/2000 = 0.482

significance level = = 0.01

Standard Deviation of = = sqrt(p*(1-p) / n )

= sqrt(0.49*(1-0.49) / 2000 )

= 0.011178

Test hypothesis :

: p = 0.49 (Null hypothesis)

: p < 0.49 (Alternative hypothesis)

Find the test statistic for this hypothesis test.

The test statistic = z_observed = (-p) /

z_observed = (0.482-0.49) / 0.011178​​​​​​​

z_observed = -0.71​​​​​​​