# Math Help - Hypothesis Testing!

1. ## Hypothesis Testing!

I need help in this statistics problem..please someone assist!

A blog hosting company claims that over 75% of its users does not limit access to their blogs in any way. A survey of 486 bloggers revealed that 370 of the respondents did not limit access. We want to test the company’s claim.
a. What are the null and alternative hypotheses?
b. What is the test statistic?
c. What is the p-value for the test?
d. What is the conclusion regarding the true proportion of bloggers that do not limit access to their blogs?

I always have difficulty understand, how to figure out the null and alternative hypothesis. And explanation would be appreciated!

Thank you very much!

2. Originally Posted by Vedicmaths
I need help in this statistics problem..please someone assist!

A blog hosting company claims that over 75% of its users does not limit access to their blogs in any way. A survey of 486 bloggers revealed that 370 of the respondents did not limit access. We want to test the company’s claim.
a. What are the null and alternative hypotheses?
b. What is the test statistic?
c. What is the p-value for the test?
d. What is the conclusion regarding the true proportion of bloggers that do not limit access to their blogs?

I always have difficulty understand, how to figure out the null and alternative hypothesis. And explanation would be appreciated!

Thank you very much!
H0: p > 0.75

H1: p < 0.75.

Sample proportion: $\hat{p} = \frac{370}{486} \approx 0.76$.

$\hat{p}$ ~ $N\left(\mu = p = 0.75, \, \sigma = \sqrt{\frac{p(1-p)}{n}} \approx 0.02\right)$.

(The true population is assumed to be 0.75).

$z = \frac{\hat{p} - \mu}{\sigma} = \frac{0.76-0.75}{0.02} = 0.5$.

p-value $= \Pr(z < 0.5) = \, ......$

To draw a conclusion you'll need to compare the p-value with the chosen significance level .....