Mathematics, 21.12.2019 04:31 katelyn0402

The national percent of adults who have a laptop computer is 62%. in san francisco, a simple random sample of 100 adults is taken and 69% of these adults have a laptop. is this strong evidence that more adults in sf have laptops than the national average?

a) state the null hypothesis and the alternative in terms of a box model.
b) find z and p values.
c) what do you conclude?

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Answer from: knighiv

a) Null hypothesis: $p\leq 0.62$

Alternative hypothesis: p 0.62

b) $z=\frac{0.69 -0.62}{\sqrt{\frac{0.62(1-0.62)}{100}}}=1.442$

p_v =P(Z1.442)=0.235

c) The p value obtained was a high low value and using the significance level assumed for example $\alpha=0.05$ we have $p_v\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults who have a laptop is not significantly higher than 0.62 .

Step-by-step explanation:

1) Data given and notation

n=100 represent the random sample taken

X represent the adults that have a laptop

$\hat p=0.69$ estimated proportion of adults that have a laptop

p_o=0.62 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 the proportion is higher than 0.62 the national proportion:

Null hypothesis: $p\leq 0.62$

Alternative hypothesis: p 0.62

When we conduct a proportion test we need to use the z statistic, 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:

$z=\frac{0.69 -0.62}{\sqrt{\frac{0.62(1-0.62)}{100}}}=1.442$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about 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.

The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

p_v =P(Z1.442)=0.235

The p value obtained was a high low value and using the significance level assumed for example $\alpha=0.05$ we have $p_v\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults who have a laptop is not significantly higher than 0.62 .

Answer from: Quest

U ok yeah u go do that

Answer from: Quest

step-by-step explanation:

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The national percent of adults who have a laptop computer is 62%. in san francisco, a simple random...