Question

You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10.

      Ho:μ=50.1Ho:μ=50.1
      Ha:μ<50.1Ha:μ<50.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=20n=20 with mean M=42.7M=42.7and a standard deviation of SD=11.4SD=11.4.

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) αα
• greater than αα

This p-value 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 50.1.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 50.1.
• The sample data support the claim that the population mean is less than 50.1.
• There is not sufficient sample evidence to support the claim that the population mean is less than 50.1.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 50.1

H_a : < 50.1

= 42.7

= 50.1

s = 11.4

n = 20

df = 20 - 1 = 19

Test statistic = t

= ( - ) / s / n

= (42.7 - 50.1) / 11.4 / 20

= -2.903

Test statistic = -2.903

P-value = 0.0046

= 0.10

P-value <

Reject the null hypothesis .

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 50.1.