Question

In a recent study of enterprise resource planning​ (ERP) system​ effectiveness, researchers asked companies how they assessed the success of their ERP systems. Out of 360 manufacturing companies​ surveyed, they found that 201 used return on investment​ (ROI), 110 used reductions in inventory​ levels,42 used improved data​ quality, and 7 used​ on-time delivery. In a survey of 860 service​ firms,470 used​ ROI,260 used inventory​ levels,100 used improved data​ quality, and 30 used​ on-time delivery. Is there evidence that the measures used to assess ERP system effectiveness differ between service and manufacturing​ firms? Perform the appropriate test and state your conclusion.

State the null and alternative hypothesis.

A. Determine the χ2 statistic. ​(Round to three decimal places as​ needed.)

B. What is the P-Value (Round answer to three decimal places as needed)

What is the proper conclusion? at the significance level x equals=0.05.

Answer 1

	response 1	response 2	response 3	response 4	row total
Group 1	201	110	42	7	360
Group 2	470	260	100	30	860
column total	671	370	142	37	1220

Here the response 1= used return on investment​ (ROI).

response 2=used reductions in inventory​ levels.

response 3=used improved data​ quality.

response 4=used​ on-time delivery.

• Step 1. Set up hypotheses and determine level of significance.

H₀: Groups and responses are independent

H₁: H₀ is false. α=0.05

• Step 2.  Select the appropriate test statistic.

The formula for the test statistic is:

.

The condition for appropriate use of the above test statistic is that each expected frequency is at least 5. In Step 4 we will compute the expected frequencies and we will ensure that the condition is met.

• Step 3. Set up decision rule.

The decision rule depends on the level of significance and the degrees of freedom, defined as df = (r-1)(c-1), where r and c are the numbers of rows and columns in the two-way data table. The row variable is the living arrangement and there are 2 arrangements considered, thus r=2. The column variable is exercise and 4 responses are considered, thus c=4. For this test, df=(2-1)(4-1)=1(3)=3. Again, with χ² tests there are no upper, lower or two-tailed tests. If the null hypothesis is true, the observed and expected frequencies will be close in value and the χ² statistic will be close to zero. If the null hypothesis is false, then the χ² statistic will be large. The rejection region for the χ² test of independence is always in the upper (right-hand) tail of the distribution. For df=3 and a 5% level of significance, the appropriate critical value is 7.81   and the decision rule is as follows: Reject H₀ if c ²> .7.81

• Step 4. Compute the test statistic.

We now compute the expected frequencies using the formula,

Expected Frequency = (Row Total * Column Total)/N.

The computations can be organized in a two-way table. The top number in each cell of the table is the observed frequency and the bottom number is the expected frequency. The expected frequencies are shown in parentheses.

	response 1	response 2	response 3	response 4	row total
Group 1	201 (198)	110 (109.18)	42 (41.90)	7 (10.91)	360
Group 2	470 (473)	260 (260.81)	100 (100.09)	30 (26.08)	860
column total	671	370	142	37	1220

Notice that the expected frequencies are taken to one decimal place and that the sums of the observed frequencies are equal to the sums of the expected frequencies in each row and column of the table.

The test statistic is computed as follows:

=

= 2.063969

• Step 5. Conclusion.

We accept H₀ because 2.063969 7.81. i.e Groups and responses are independent.