Question

You wish to test the following claim (Ha) at a significance level of α = 0.05.

Ho: μ = 58.9

Ha: μ < 58.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 34 with mean M = 54.2 and a standard deviation of SD = 8.3.

1. What is the test statistic for this sample? (Report answer accurate to THREE decimal places.)
test statistic =
2. What is the p-value for this sample? (Report answer accurate to THREE decimal places.)
p-value =
3. The p-value is...

a. less than (or equal to) αα

b. greater than αα

4. This test statistic leads to a decision to...

a. reject the null

b. accept the null

c. fail to reject the null

5. As such, the final conclusion is that...

a. There is sufficient evidence to warrant rejection of the claim that the population mean is less than 58.9.

b. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 58.9.

c.The sample data support the claim that the population mean is less than 58.9.

d. There is not sufficient sample evidence to support the claim that the population mean is less than 58.9.

Answer 1

Solution :

= 58.9

= M = 54.2

S= 8.3

n = 34

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 58.9

H_a : < 58.9

1) Test statistic = t

= ( - ) / s / n

= (54.2 - 58.9) /8.3 / 34

= -3.302

2) P(z < -3.302 ) = 0.001

P-value = 0.001

= 0.05  

c)P-value <

p = 0.001 < 0.05, it is concluded that the null hypothesis is rejected.

4) Reject the null hypothesis .

5) There is sufficient evidence to warrant rejection of the claim that the population mean μ is less than 58.9