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

$H_o:\mu =67.9$ $H_a:\mu \ne 67.9$

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 13 with mean M = 73 and a standard deviation of SD = 14.2.

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…

• 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 not equal to 67.9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 67.9.
• The sample data support the claim that the population mean is not equal to 67.9.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 67.9.

Answer :

Given :

Hypothesized Population Mean $(\mu )=67.9$

Sample Standard Deviation $(s)=14.2$

Sample Size $(n)=13$

Sample Mean $(x\overline{)}=73$

Significance Level $(\alpha )=0.10$

Solution :

The null and alternative hypothesis :

$$H_o:\mu =67.9$$ $$H_a:\mu \ne 67.9$$

The test statistic :

$$t=\frac{\overline{x}–\mu }{\frac{s}{\sqrt{n}}}=\frac{73–67.9}{\frac{14.2}{\sqrt{13}}}=1.295$$

The degree of freedom is calculated as :

$$\text{df}=n–1=13–1=12$$

The p-value is calculated as :

$$\text{The p-value}=2\times \text{P}(t>1.295)=0.2197$$

The p-value is greater than α

This test statistics leads to a decision to fail to reject the null

As, such the final conclusion is that

→ The correct option is (B)