The pooled estimate of the variance is 187.650 and the test statistic is -2.32
<h3>Pooled estimate of the variance</h3>The dataset is given as:
Regular price 138 124 89 112 116 123 98
Reduced price 124 134 154 135 118 126 133 132
Let the regular price be dataset 1 and the reduced price be dataset 2.
So, we have:
#1: 138 124 89 112 116 123 98
#2: 124 134 154 135 118 126 133 132
Calculate the sample means and the sample standard deviations using a graphing calculator.
<u>#1</u>
<u>#2</u>
The pooled estimate of the variance is:
This gives
Evaluate the factors
Divide
Hence, the pooled estimate of the variance is 187.650
<h3>The test statistic</h3>This is calculated using:
This gives
This gives
Evaluate the product
Evaluate the exponent
Divide
t = -2.32
Hence, the test statistic is -2.32
<h3>The decision about the null hypothesis</h3>The critical value at 0.025 significance level is -1.96
-2.32 is less than -1.96
This means that we accept the null hypothesis
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