Question

You wish to test the following claim ( H 1 ) at a significance level of α = 0.01 . H o : μ = 83.3 H 1 : μ < 83.3 You believe the population is normally distributed and you know the standard deviation is σ = 15.5 . You obtain a sample mean of M = 81.5 for a sample of size n = 19 . 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... less than (or equal to) α greater than α This test statistic 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 population mean is less than 83.3. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 83.3. The sample data support the claim that the population mean is less than 83.3. There is not sufficient sample evidence to support the claim that the population mean is less than 83.3

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 83.3

H_a : < 83.3

= 81.5

= 83.3

= 15.5

n = 19

Test statistic = z

= ( - ) / / n

= (81.5 - 83.3) / 15.5 / 19

= -0.506

Test statistic = -0.506

P(z < -0.506) = 0.3064

P-value = 0.3064

= 0.01

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 83.3.