Reference no: EM132340631

Question

13% of all Americans suffer from sleep apnea. A researcher suspects that a different percentage of those who live in the inner city have sleep apnea. Of the 331 people from the inner city surveyed, 30 of them suffered from sleep apnea. What can be concluded at the level of significance of α = 0.05?

a.) For this study, we should use the z-test or t-test?

b.) The null and alternative hypotheses would be:   

H₀:_____ ____ ____ enter a decimal

H₁:_____ ____ ____ enter a decimal

c,) The test statistic_____=______ three decimal places

d.) the p-value=_____four decimal places

e.) The p value is?

f.) Based on this we should either reject, accept or fail to reject the null hypothesis?

g.) Thus, the final conclusion is that ...

1.) The data suggest the populaton proportion is significantly different from 13% at α= 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is different from 13%

2.) The data suggest the population proportion is not significantly different from 13% at α = 0.05, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is different from 13%.

3.) The data suggest the population proportion is not significantly different from 13% at α= 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 13%.

H.) Interpret the p-value in the context of the study.

1.) If the sample proportion of inner city residents who have sleep apnea is 9% and if another 331 inner city residents are surveyed then there would be a 3.32% chance that we would conclude either fewer than 13% of all inner city residents have sleep apnea or more than 13% of all inner city residents have sleep apnea.

2.) There is a 3.32% chance of a Type I error.

3.) There is a 3.32% chance that the percent of all inner city residents have sleep apnea differs from 13%.

4.) If the population proportion of inner city residents who have sleep apnea is 13% and if another 331 inner city residents are surveyed then there would be a 3.32% chance that either fewer than 9% of the 331 inner city residents surveyed have sleep apnea or more than 17% of the 331 inner city residents have sleep apnea.

I.) Interpret the level of significance in the context of the study.

1.) There is a 5% chance that the proportion of all inner city residents who have sleep apnea is different from 13%.

2.) If the population proportion of inner city residents who have sleep apnea is different from 13% and if another 331 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 13%.

3.) If the population proportion of inner city residents who have sleep apnea is 13% and if another 331 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is different from 13%.

4.) There is a 5% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.