Question

You wish to test the following claim ( H a ) at a significance level of α = 0.05 . H o : μ = 73.7 H a : μ < 73.7 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 107 mean: M = 69.7 standard deviation: S D = 10.2 . What is the test statistic for this sample? (Round the answer accurate to 3 decimal places.) test statistic: t = What is the P-value for this sample? (Round the answer accurate to 3 decimal places.) P-value = The P-value is... less than (or equal to) α greater than α This leads to a decision to... reject the null accept the null fail to reject the null So, the final conclusion is that... The data do not support the claim of the alternative hypothesis that the population mean is less than 73.7. The sample data support the claim of the alternative hypothesis that the population mean is less than 73.7

Answer 1

Solution :

Given that ,

= 73.7

M = 69.7

s = 10.2

n = 107

The null and alternative hypothesis is ,

H₀ :   = 73.7

H_a : < 73.7

This is the left tailed test .

Test statistic = t

= (M - ) / s / n

= ( 69.7 - 73.7) / 10.2 / 107

= -4.057

The test statistic = -4.057

df = n - 1 = 107 - 1 = 106

P-value = ( t_{-4.057,106 )} = 0.000

P-value = 0.000

= 0.05  

0.000 < 0.05

P-value <

The P-value is less than

Reject the null hypothesis .

Conclusion : - The sample data support the claim of the alternative hypothesis that the population mean is less than 73.7