According to a Pew Research Center study, in May 2011, 35% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.

She selects 300 community college students at random and finds that 120 of them have a smart phone. In testing the hypotheses H0: p = 0.35 versus Ha: p > 0.35, she calculates the test statistic as Z = 1.82. Assume the significance level is ? = 0.10.

Which of the following is an appropriate conclusion for the hypothesis test?

There is enough evidence to show that more than 35% of community college students own a smart phone (P?value = 0.034).

There is enough evidence to show that more than 35% of community college students own a smart phone (P?value = 0.068).

There is not enough evidence to show that more than 35% of community college students own a smart phone (P?value = 0.966).

There is not enough evidence to show that more than 35% of community college students own a smart phone (P?value = 0.034).

Does secondhand smoke increase the risk of a low weight birth? A baby is "low birth weight" if it weighs less than 5.5 pounds at birth. According to the National Center of Health Statistics, about 7.8% of all babies born in the U.S. are categorized as low birth weight. Researchers randomly select 1200 babies whose mothers had extensive exposure to secondhand smoke during pregnancy. 10.4% of the sample are categorized as low birth weight.

Answer the following:

Which of the following are the appropriate null and alternative hypotheses for this research question.

H0: p = 0.078; Ha: p ? 0.078

H0: p = 0.078; Ha: p > 0.078

H0: p = 0.104; Ha: p ? 0.104

H0: ? = 0.104; Ha: ? > 0.104

So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis

And the best conclusion would be:

There is enough evidence to show that more than 35% of community college students own a smart phone (Pvalue = 0.034).

And for the second case the correct system of hypothesis is:

H0: p = 0.078; Ha: p > 0.078

Step-by-step explanation:

Data given and notation

n=300 represent the random sample taken

[tex]\hat p=\frac{120}{300}=0.4[/tex] estimated proportion of college students that have a smart phone

[tex]p_o=0.35[/tex] is the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion is >0.35.:

Null hypothesis:[tex]p\leq 0.35[/tex]

Alternative hypothesis:[tex]p > 0.35[/tex]

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

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)

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

Calculate the statistic

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

[tex]z=\frac{0.4 -0.35}{\sqrt{\frac{0.35(1-0.35)}{300}}}=1.82[/tex]

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 significance level provided [tex]\alpha=0.1[/tex]. The next step would be calculate the p value for this test.

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

[tex]p_v =P(z>1.82)=0.034[/tex]

So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis

And the best conclusion would be:

There is enough evidence to show that more than 35% of community college students own a smart phone (Pvalue = 0.034).

And for the second case the correct system of hypothesis is:

H0: p = 0.078; Ha: p > 0.078

topeadeniran2 topeadeniran2 · Answer 2 · 2022-04-05T15:35:31+02:00

The conclusion for the hypothesis testing is that A. There is enough evidence to show that more than 35% of community college students own a smart phone (P = 0.034).

How to deduce the hypothesis?

From the information given, the z value is 1.82 and the appropriate p value is 0.034. Therefore, one should reject the null hypothesis.

This illustrates that there's enough evidence to show that more than 35% of community college students own a smart phone.

The appropriate null and alternative hypotheses for this research question for the case about smoking is H0: p = 0.078; Ha: p > 0.078.

Learn more about hypothesis on:

https://brainly.com/question/11555274