Question

For the answer please show you work : please include steps/functions used on TI 84+ calculator (mandatory).

a. State the hypotheses and identify the claim.

b. Find the critical value.

c. Compute the test value.

d. Make the decision./Summarize the results

In a magazine survey, 60% of respondents said that they used reusable shopping bags, 32% asked for plastic, and 8% requested paper. A random sample of 300 shoppers revealed that 28 asked for paper, 120 requested plastic, and the remaining shoppers had reusable bags. At alpha= 0.01, does this differ from the results of the survey?

Answer 1

Solution:

Given:

	Observed counts	Expected Percentage
Reusable shopping bags	152	60%
Plastic	120	32%
Paper	28	8%

Level of significance =

We have to test if observed counts are different from expected counts.

Part a) State the hypotheses and identify the claim.

H0: The result of the survey is same as expected percentages. That is: the observed count distribution is same expected counts.

Vs

H1: The result of the survey is different from expected percentages. That is : the observed count distribution is different from expected counts.

Part b) Find the critical value.

df = k - 1 = 3- 1 = 2

Level of significance =

Look in Chi-square table for df = 2 and right tailed area = 0.01 and find Chi-square critical value.

Chi-square critical value = 9.210

Part c. Compute the test value.

We use TI 84 plus calculator to find Chi-square test statistic value.

Before that we need to find expected counts by using given expected percentage values.

We multiply N = 300 by given percentage value to get Expected counts.

Thus we get:

	Observed counts	Calculations	Expected Counts
Reusable shopping bags	152	=300 X 0.60	180
Plastic	120	=300 X 0.32	96
Paper	28	=300 X 0.08	24
	300

Use following steps in TI 84:

Step 1) Press STAT and select EDIT

Step 2) Under EDIT , select L1 and L2 column

Delete all numbers under L1 and L2 column

Under L1 column Enter Observed counts and Under L2 enter Expected Counts

Step 3) Now press STAT and select TESTS

Step 4) Under TESTS , select - GOF Test.

Step 4) Under -GOF Test, select L1 for Observed and L2 for Expected

( Note: L1 and L2 is already there, if not , press 2ND and 1 for L1 and 2ND and 2 for L2.)

df = 2

Click on calculate and press Enter.

Thus we get:

test statistic value = 11.022

Part d. Make the decision./Summarize the results

Decision Rule: Reject H0, if test statistic value > critical value, otherwise we fail to reject H0,

Since test statistic value = 11.022 > critical value = 9.210, we reject H0.

Thus we conclude that: the result of the survey is different from expected percentages.