Question

Old Billie is very excited for Letecia, but she is also worried about her. So she conducts a poll of 400 Avocado Park residents who have gone on a first date in the last month, asking them if they are glad they did and 287 of them said that they were. Old Billie has decided that she will stop the date from happening if there is less than a 75% chance that Letecia will be happy. Hadey tells her she is being extra, so she settles on a significance level of 0.01 to be safe.

f. What assumptions must you make to perform a test on the null hypothesis you chose in part d?

g. Calculate the P-Value and make a decision about the null hypothesis based on it.

h. Summarize your decision from part f.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.75

Ha : p < 0.75

n = 400

x = 287

= x / n = 287 / 400 =0.72

P0 = 0.75

1 - P0 = 1 - 0.75 = 0.25

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.72 - 0.75 / [(0.75*0.25) / 400]

= -1.50

Test statistic = z = -1.50

P(z < -1.50 ) = 0.0668

P-value =  0.0668

= 0.01

P-value >

0.0668 > 0.01

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that