For each of the following problems, you should do the following: a. State the nu

Question

For each of the following problems, you should do the following:

a. State the null and alternative hypotheses. Use symbols and numbers, not words.

For example, p > .42 or µ = 22 or p .37. [You can find the symbols you need in Word by going to Insert, Symbol.] [HINT: p is the symbol for proportion, not percentage.]

b. Determine whether the data satisfy the conditions which allow you to use the z-test for the population proportion. [Hint: You should include 3 things you checked to see whether the Z test was appropriate. Even if it is not appropriate, you should continue with the rest of the steps.]

c. Show your work for the calculation of the test statistic, z.

d. Find the p-value of the test statistic either by using Excel or the z-table in your text. [Hint: Be careful about whether you are looking for the area above or below the z-value - - that would be determined by the sign (> or <) in Ha. Be especially careful if the sign in Ha is .]

e. State your statistical decision (reject Ho or do not reject Ho).

f. Did you find the evidence the problem was looking for?

1. In the past, 83% of American adults said that owning their own home was an extremely important goal. In a recent survey of 50 randomly selected adults, 40 said that owning their own home was an extremely important goal. Is there sufficient evidence (at the 0.10 level of significance) to conclude that the proportion has changed?

Ho:                                Ha:

Are conditions satisfied? Explain (See #2 in the instructions above).

What is value of the test statistic? (Show your work.)

What is the p-value?

Interpret the p-value in the context of the problem:

Statistical decision:

Did you find the evidence the problem was looking for?

1. In the past, 83% of American adults said that owning their own home was an extremely important goal. In a recent survey of 50 randomly selected adults, 40 said that owning their own home was an extremely important goal. Is there sufficient evidence (at the 0.10 level of significance) to conclude that the proportion has changed?

Ho:                                Ha:

Are conditions satisfied? Explain (See #2 in the instructions above).

What is value of the test statistic? (Show your work.)

What is the p-value?

Interpret the p-value in the context of the problem:

Statistical decision:

Did you find the evidence the problem was looking for?

Explanation / Answer

Ho: p=0.83

HA:p0.83

std error =(p(1-p)/n)1/2 =0.053

phat=40/50=0.8

hence test stat z=(phat-p)/std error =(0.83-0.8)/0.053=-0.5647

p value =0.5723

p value is the extreme probability for which null hypothesis holds true.

As p vlaue is greater then 0.1 level we can not conclude that the proportion has changed

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