Question

A poll printed the results of a survey of 880 Americans focusing on their perception of the quality of Japanese products. It has been observed that the sentiment towards Japanese products has actually improved over time. Is there sufficient evidence to conclude that American sentiment towards Japanese products changed from 1999 to 2005? 1999 2005 Good to Excellent | 24 % | 25 % 26 % | 28 % Below Average | 21 % | 18% No Opinion | 29 % | 29 % Opinion Average Copy Data Step 4 of 10: Find the expected value for the number of Americans who rate Japanese products good to excellent Round your answer to two decimal places Keypad 2 Points Answer(How to Enter) Step 5 of 10: Find the expected value for the number of Americans who rate Japanese products average. Round your answer to two decimal places Answer(How to Enter) 2 Points Keypad Average Step 6 of 10: Find the value of the test statistic. Round your answer to three decimal places. 2 Points Keypad Answer(How to Enter) Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem. Answer(How to Enter) 2 Points Keypad Step 8 of 10: Find the critical value of the test at the 0.1 level of significance. Round your answer to three decimal places Keypad 2 Points Answer(How to Enter) Step 9 of 10: Make the decision to reject or fail to reject the null hypothesis at the 0.1 level of significance. Answer 2 Points Keypad Fail to Reject Null Hypothesis Reject Null Hypothesis Step 10 of 10: State the conclusion of the hypothesis test at the 0.1 level of significance. Keypad Answer 2 Points There is not enough evidence to conclude that American sentiment 1999 to 2005 There is enough evidence to conclude that American sentiment towards Japanese products changed from 1999 to 2005.

Answer 1

SOLUTION

3)

H_A:At least one category has different proportion from expected above distribution.

	1999	2005	Observed	Expected	(fo-fe)^2/fe
Good to excellent	24.00%	25.00%	220	211.2	0.367
average	26.00%	28.00%	246.4	228.8	1.354
below average	21.00%	18.00%	158.4	184.8	3.7714
No opinion	29.00%	29.00%	255.2	255.2	0.000
Total			880	880	5.4924

4)

Expected count=880*0.22=211.2

5)

Expected count=880*0.26=228.8

6)

Test statistic=5.4924

7)df=4-1=3

8)

critical chi square value=CHIINV(0.025,3)=9.348

9)

As,test statistic is greater than critical value,so reject the null hypothesis.

10)There is sufficient evidence to conclude that American sentiment towards Japanese products has changed from 1999 to 2005.