Question

use a t - test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. assume the population is normally distributed.
claim: μ≠28; α = 0.10 sample statistics: \\( \overline { x } = 28.9 \\), s = 4.8, n = 13
\\( h _ { a } : \mu \
eq 28 \\) \\( h _ { a } : \mu > 28 \\)
c. \\( h _ { 0 } : \mu \
eq 28 \\) d. \\( h _ { 0 } : \mu \geq 28 \\)
\\( h _ { a } : \mu = 28 \\) \\( h _ { a } : \mu < 28 \\)
what is the value of the standardized test statistic?
the standardized test statistic is 0.68. (round to two decimal places as needed.)
what is the p - value of the test statistic?
p - value = 0.508 (round to three decimal places as needed.)
decide whether to reject or fail to reject the null hypothesis.
a. reject \\( h _ { 0 } \\). there is not enough evidence to support the claim.
b. reject \\( h _ { 0 } \\). there is enough evidence to support the claim.
c. fail to reject \\( h _ { 0 } \\). there is not enough evidence to support the claim.
d. fail to reject \\( h _ { 0 } \\). there is enough evidence to support the claim.

Explanation:

Step1: Determine the null and alternative hypotheses

The claim is $\mu
eq28$. So, the null hypothesis $H_0:\mu = 28$ and the alternative hypothesis $H_a:\mu
eq28$.

Step2: Compare the P - value with the significance level

We are given $\alpha=0.10$ and the P - value $=0.508$. Since $P - value=0.508>0.10=\alpha$.

Answer:

C. Fail to reject $H_0$. There is not enough evidence to support the claim.