Question

Carolina, Inc. has three stores located in three different area. Random samples of the sales of the three stores (in $1000) are shown below. Note that the sample sizes are not equal. We want to conduct an ANOVA test to determine if the means of the three populations are equal.

Store 1 Store 2 Store 3

87 75 84

84 78 67

88 60   58

82 62

(1) Compute the overall mean.

(2) State the null and alternative hypotheses to be tested, using appropriate mathematical notation.

(3) The null hypothesis is to be tested at 95% confidence. Show all of your calculations and justifications to use the p-value approach for this hypothesis.

(4) Use the critical value approach for this hypothesis again.

(5) Create the ANOVA table for this hypothesis.

Answer 1

ANSWER:

I use Excel for calculations. The output is given below.

D overall mean 341 + 2.75 +209 = 75 11 MisMe and are 2) het My be the means auto sales of store i, store 2 and store 3 respectively. Then hypothesis Ho : p = f = 4₂ Ha atleast one of the mean & sales is ditterent from others. where Ho is null hypothesis and HA is altemative hypothesis. 3) Here P-value PLF74.282556) = 0.054398 >0.05 we tail to reject Ho. A) Here Fc4.282556 2 F critic = 4.45897. this implies we tail to reject Ho. a=0.05 F = 4:282556 , and
Answer for (5) is given in Excel output.

Please comment if you have any doubts.

For calculations in Excel you follow the steps.

1)Enter data

2)Data-->Data Analysis-->Single Factor ANOVA-->Select all data without heading. Then mention the output range.-->Ok

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