Are you an impulse shopper?A survey of 800 grocery shoppers indicated that 53%of males and 44%of females make an impulse purchase every time they shop.Assume that the survey consisted of 400 males and 400 females. a.At the 0.05 level of significance , the value of the test statistic.
Question
Are you an impulse shopper?A survey of 800 grocery shoppers indicated that 53%of males and 44%of females make an impulse purchase every time they shop.Assume that the survey consisted of 400 males and 400 females. a.At the 0.05 level of significance , the value of the test statistic.
Solution
To answer this question, we need to perform a hypothesis test for the difference between two proportions. Here are the steps:
Step 1: State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: p1 = p2 (The proportion of males who are impulse shoppers is equal to the proportion of females who are impulse shoppers)
Alternative hypothesis: p1 ≠ p2 (The proportion of males who are impulse shoppers is not equal to the proportion of females who are impulse shoppers)
Step 2: Formulate an analysis plan. For this analysis, the significance level is defined as 0.05. The test statistic is a z-score (z).
Step 3: Calculate the test statistic.
We have:
n1 = 400 (number of males) x1 = 0.53 * 400 = 212 (number of males who are impulse shoppers) p̂1 = x1/n1 = 212/400 = 0.53 (sample proportion of males who are impulse shoppers)
n2 = 400 (number of females) x2 = 0.44 * 400 = 176 (number of females who are impulse shoppers) p̂2 = x2/n2 = 176/400 = 0.44 (sample proportion of females who are impulse shoppers)
We also need to calculate the pooled sample proportion (p) and the standard error (SE). Using the formulas:
p = (x1 + x2) / (n1 + n2) = (212 + 176) / (400 + 400) = 0.485
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = sqrt{ 0.485 * (1 - 0.485) * [ (1/400) + (1/400) ] } = 0.050
The test statistic (z) is then calculated as:
z = (p̂1 - p̂2) / SE = (0.53 - 0.44) / 0.050 = 1.8
So, at the 0.05 level of significance, the value of the test statistic is 1.8.
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