Question

In a recent survey of 514 dating experts, 463 said that humor in the first five minutes is most important for a good first impression. Test the claim that more than 88% of all dating experts say that humor in the first five minutes is most important for a good first impression. What are the p-value and the overall conclusion?

Group of answer choices

p-value = 0.0736, sufficient evidence to support the claim

p-value = 0.0736, not sufficient evidence to support the claim

p-value = 0.1472, sufficient evidence to support the claim

p-value = 0.1472, not sufficient evidence to support the claim

Answer 1

Solution :

Given that ,

n = 514

x = 463

The null and alternative hypothesis is ,

H₀ : p = 0.88

H_a : p > 0.88

This is the right tailed test .

= x / n = 463 / 514 = 0.9008

P₀ =  88% = 0.88

1 - P₀ = 1 - 0.88 = 0.12

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.9008 - 0.88 / [0.88 ( 1 - 0.88 ) / 514 ]

= 1.45

The test statistic = 1.45

P-value = 0.0736

= 0.05  

0.0736 > 0.05  

P-value >  

Fail to reject the null hypothesis .

There is not sufficient evidence to support the claim ,

Correct option : - p-value = 0.0736, not sufficient evidence to support the claim