Question

You are conducting a study to see if the probability of being hit by lightning is significantly less than 0.79. You use a significance level of α=0.002.

H0:p=0.79
H1:p<0.79

You obtain a sample of size n=389 in which there are 302 successes.

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

less than (or equal to) α

greater than α

This p-value leads to a decision to...

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the probability of being hit by lightning is less than 0.79.
There is not sufficient evidence to warrant rejection of the claim that the probability of being hit by lightning is less than 0.79.
The sample data support the claim that the probability of being hit by lightning is less than 0.79.
There is not sufficient sample evidence to support the claim that the probability of being hit by lightning is less than 0.79.

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H₀ : p = 0.79
H_A : p < 0.79

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	302	389	0.77634961	0.020651347	-0.66099249	0.2543

Hence,

p - Value = 0.2543

The p-value is greater than α.

This p-value leads to a decision to fail to reject the null.

Final conclusion: There is not sufficient sample evidence to support the claim that the probability of being hit by lightning is less than 0.79. Option D is correct.