# According to the Pew Research Center,on the propotion of the American population who use only a cellular telephone (landline) is 0.37. Jason conducts a survey of one hundred fifty 20 to 24 year olds who live on their own and finds that 73 do not have a landline to their home. Does this provide sufficient evidence to conclude that the proportion of 20 to 24 year olds who live on their own and don't have a landline is greater than 0.37? Use a=0.10 level of significance.D) Compute the test statistic z0. Round to the nearest hundredth.E) Draw a normal model with the area that represents the P-value shaded.F) Determine and interpret the P-value. What is the conclusion of the hypothesis test?

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According to the Pew Research Center,on the propotion of the American population who use only a cellular telephone (landline) is 0.37. Jason conducts a survey of one hundred fifty 20 to 24 year olds who live on their own and finds that 73 do not have a landline to their home. Does this provide sufficient evidence to conclude that the proportion of 20 to 24 year olds who live on their own and don't have a landline is greater than 0.37? Use a=0.10 level of significance.

D) Compute the test statistic z0. Round to the nearest hundredth.

E) Draw a normal model with the area that represents the P-value shaded.

F) Determine and interpret the P-value. What is the conclusion of the hypothesis test?

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Step 1

Solution:

Part(D):Finding the test statistic value for the hypothesis test for proportion:

Hypotheses:

Let p be the population proportion of American who live on their own and do not have landline. The aim is to check whether the proportion of American who live on their own and do not have landline is greater than 0.37. The null and the alternative hypothesis is,

H0 : p = 0.37 vs Ha : p > 0.37.

Step 2

Test statistic:

A sample of 150 20 to 24 year olds who live on their own has been taken. Out of 150, 73 American who olds 20 to 24 were found to not have a land line. That is, n = 150 and x =73. Therefore, the sample proportion p-cap is 73 / 150 = 0.49.The hypothetical proportion, p0 is 0.37.  The level of significance,α=0.10. The test statistic for hypothesis test for proportion is given by:

Step 3

Part(E)Sketch the normal model with the area that represent...

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