Question

many people believe that the average number of facebook friends is 130. the population standard deviation is 38. a random sample of 40 high school students in a particular county revealed that the average number of facebook friends was 153. at \\( \alpha = 0.10 \\), is there sufficient evidence to conclude that the mean number of friends is greater than 130?
part 1 of 5
state the hypotheses and identify the claim with the correct hypothesis.
\\( h _ { 0 } : \mu = 130 \\) not claim
\\( h _ { 1 } : \mu > 130 \\) claim
this hypotheses test is a one - tailed test.
part: \\( 1 / 5 \\)
part 2 of 5
find the critical value(s). round the answer to two decimal places. if there is more than one critical value, separate them with commas.
critical value(s):

Explanation:

Step1: Determine the type of test

This is a one - tailed (right - tailed) test with significance level $\alpha = 0.10$.

Step2: Find the critical value

For a one - tailed $z$ - test with $\alpha=0.10$, we look up the value in the standard normal distribution table. The critical value $z_{\alpha}$ is the value such that $P(Z>z_{\alpha})=\alpha$. Using the standard normal distribution table or a calculator with a normal distribution function (e.g., in Excel: =NORM.S.INV(1 - 0.1)), we get $z = 1.28$.

Answer:

$1.28$