Question

You wish to test the following claim (Ha) at a significance level of a = 0.002 H:= 76.5 H:<76.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 86 with mean M = 74.3 and a standard deviation of SD= 6.2. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic What is the p-value for this sample? (Report answer accurate to four decimal places.) P-value = The p-value is... O less than (or equal to) a Ogreater than a This test statistic leads to a decision to... Oreject the null O accept the null O fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is less than 76.5. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 76.5. The sample data support the claim that the population mean is less than 76.5. There is not sufficient sample evidence to support the claim that the population mean is less than 76.5.

Answer 1

Solution :

$\mu$= 76.5

M =74.3

$\sigma$ =6.2

n = 86

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$  = 76.5

H_a : $\mu$ < 76.5

Test statistic = z

= (M - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (74.3 -76.5) / 6.2 / $\sqrt$ 86

= -3.291

Test statistic = z = -3.291

P(z < -3.291 ) = 0.0005

P-value = 0.0005

$\alpha$ = 0.002

P-value < $\alpha$

0.0005 < 0.02

Reject the null hypothesis .

There is sufficient evidence to warrent rejection of the claim that the population mean is less than 76.5