Question

The manufacturer of an over-the-counter pain reliever claims that its product brings pain relief to headache suffers in less than 3.5 minutes, on average. In order to be able to make this claim in its television advertisements, the manufacturer was required by a particular television network to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 headache sufferers, the mean time to relief was 3.11 minutes and the standard deviation was 69.84 seconds.

Does this data support the manufacturer's claim of less than 3.5 minutes? Set up the appropriate hypotheses test procedure. Test using alpha = 0.05.

I need help obtaining the P-value for the test. Link to an image of the question below.

https://gyazo.com/96e3227862379dba7b28f5ee586aea43

Answer 1

Solution :

= 3.5

= 3.11

= 69.84 second = 1.164 minutes

n = 50

This is the left tailed test .

The null and alternative hypothesis is

H₀ :   = 3.5

H_a : < 3.5

Test statistic = z

= ( - ) / / n

= (3.11-3.5) /1.164 / 50

= -2.369

P (Z < -2.369 ) = 0.0089

P-value = 0.0089

= 0.05  

p=0.0089<0.05,

Reject the null hypothesis .

There is sufficient evidence to suggest that