A survey of the DVD market research has shown that 17% of American families own

Question

A survey of the DVD market research has shown that 17% of American families own DVD players. California Board of Commerce believes the figure is higher for California. To test whether this figure is higher than 17%, the board contacted a random sample of 550 families in California and asked whether they owned a DVD player. Suppose 115 replied that they owned a DVD player. Using level of significance of 10%, test whether the percentage of California families owning a DVD player is higher than rest of USA. Which of the following is the appropriate test of hypothesis to make this determination?

Select one:

A.

B.

C.

D.

E.

F. None of the above answers is correct

2.

what is test statistic value for this test of hypothesis problem?

Select one:

A. 1.44

B. 2.44

C. 2.94

D. 3.44

E. None of the above answers is correct

3.

what is(are) the critical value(s) for this test of hypothesis problem?

Select one:

A. -1.28

B. 1.28

C. 1.96

D. -1.96

F. None of the above answers is correct

4.

based on the values of sample test statistic and critical value(s) of test statistic, do the percentage of families in California owning a DVD player higher than rest of USA?

Select one:

A. yes

B. no

C. there is not enough information to make this determination

D. None of the above answers is correct

5.

Null hypothesis will be rejected if p-value is greater than problem specified significance level.

Select one:

A. true

B. false

Explanation / Answer

1.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.17
Ha:   p   >   0.17 [ANSWER, B]

***********************

2.

As we see, the hypothesized po =   0.17      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.209090909      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.016017036      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    2.44   [ANSWER, B]

**************************

3.

As this is a right tailed 0.1 level test,

zcrit = 1.28 [ANSWER, B]

***************************

4.  
          
As z > 1.28, we reject Ho.

Thus,OPTION A: YES. [ANSWER, A]

*************************

5.

FALSE. We reject Ho if P < significance level.

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