Connect with a global community of knowledgeable individuals on IDNLearn.com. Ask anything and receive comprehensive, well-informed responses from our dedicated team of experts.
Sagot :
Answer:
0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.
Step-by-step explanation:
Conduct a test to determine whether the true proportion of interest is higher than 0.7.
This means that the null hypothesis is: [tex]H_{0}: p = 0.7[/tex]
And the alternate hypothesis is: [tex]H_{a}: p > 0.7[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.7 is tested at the null hypothesis:
This means that [tex]\mu = 0.7, \sigma = \sqrt{0.7*0.3}[/tex]
The sociologist found that 375 of the 500 travelers randomly selected and interviewed indicated that the airports were safe.
This means that [tex]n = 500, X = \frac{375}{500} = 0.75[/tex]
Value of the z-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.75 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{350}}}[/tex]
[tex]z = 2.44[/tex]
P-value of the test:
Probability of z being larger than 2.44, that is, a proportion larger than 0.75.
This is, looking at the z-table, 1 subtracted by the pvalue of Z = 2.44. S
Z = 2.44 has a pvalue of 0.9927
1 - 0.9927 = 0.0073
0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.
