Question

A nationwide random sample of university professors revealed that 30 professors consumed a total of 7,500 mg of caffeine daily, with a standard deviation of 40 mg. Assuming that the amount of caffeine consumed per person per day is normally distributed, an administrator wants to know if there is enough evidence to conclude that the average amount of caffeine consumed per day by university professors is more than 240 mg using α = 0.05?

Hypothesis test H0: Versus H1:

Using the p value method, the test statistical is?

The P value is?

What is the decision?

What is the conclusion?

Answer 1

Here sample size,n= 30

Total consumed caffine = 7500 for 30 so mean = 7500/30

Sample mean xbar= 7500/30 = 250

Sample standard deviation ,s =40

We need to test the claim that population mean, mu>240

So H0: mu = 240 against H1: mu > 240

It is a right tailed test

Since population Standard deviation is unknown,we use t test for one sample mean

Test statistic ,t = ( xbar - mu) / ( s/√n) = (250-240) / ( 40/√30) = 1.369

Using the P-value approach: The p-value is p = 0.0907, and since p = 0.0907≥.05, it is concluded that the null hypothesis is not rejected.

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean mu is greater than 240, at the .05 significance level.

So there is no enough evidence to conclude that the average amount of caffeine consumed per day by university professors is more than 240 mg using α = 0.05