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?

Answers: 2

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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

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

Answer from: Quest

the length of o'p' is $1.5\times op$ .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

$k=\frac{o'p'}{op}$

the scale factor is 1.5.

$1.5=\frac{o'p'}{op}$

multiply both sides by op.

$1.5\times op=o'p'$

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is $1.5\times op$ .

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