Mathematics, 30.11.2019 05:31 tommyaberman

When 3010 adults were surveyed in a poll, 27% said that they use the internet. is it okay for a newspaper reporter to write that "1 divided by 4 of all adults use the internet"? why or why not? identify the null hypothesis, alternative hypothesis, test statistic, p-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. use the p-value method. use the normal distribution as an approximation of the binomial distribution.
the test statistic is z = ? . (round to two decimal places as needed.)the p-value is ? . (round to four decimal places as needed.)identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim. (assume a 0.05 significance level.)

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Answer from: natalieagustinlop54

Null hypothesis: p=0.25

Alternative hypothesis: $p \neq 0.25$

z=2.53

pv=0.0114

So based on the p value obtained and using the significance given $\alpha=0.05$ we have p_v so we can conclude that we reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they use the Internet differs from 0.25 or 25% .

Step-by-step explanation:

1) Data given and notation

n=3010 represent the random sample taken

X represent the people who says that said that they use the Internet.

$\hat p=\frac{X}{106}=0.27$ estimated proportion of people who says that said that they use the Internet.

p_o=0.25 is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that 50% of people who says that they would watch one of the television shows.:

Null hypothesis: p=0.25

Alternative hypothesis: $p \neq 0.25$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value p_o .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.27 -0.25}{\sqrt{\frac{0.25(1-0.25)}{3010}}}=2.53$

4) Statistical decision

P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

We have the significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

p_v =2*P(z2.53)=2*(0.0057)=0.0114