Question 2 2. The past records of a supermarket show that its customers spend an

Question

Question 2 2. The past records of a supermarket show that its customers spend an average of $65 per visit at this store. To check if this is true, a sample of 12 customers were taken which reveals the following data. The data provides the money (in dollars) spent by these customers at this supermarket during their visits 88 69 141 28 106 45 32 51 78 54 110 83 Assume that the money spent by all customers at this supermarket has a normal distribution. Using 1% significance level, can you conclude that the mean amount of money spent by all customers at this supermarket is higher than $65?

Explanation / Answer

Solution:

Here, we have to use one sample t test for population mean. We have to check whether the mean amount of money spent by all customers at this supermarket is higher than $65 or not. The null and alternative hypotheses are given as below:

Null hypothesis: H0: The mean amount of money spent by all customers at this supermarket is $65.

Alternative hypothesis: Ha: The mean amount of money spent by all customers at this supermarket is higher than $65.

H0: µ =65 versus Ha: µ > 65

This is a one tailed test. (Upper tailed or right tailed test)

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

Sample size = n = 12

Sample mean = Xbar = 73.75

Sample standard deviation = S = 34.08

Level of significance = = 0.01

Degrees of freedom = df = n – 1 = 11

Upper critical value = 2.7181

t = (73.75 – 65) / [34.08/sqrt(12)]

t = (73.75 – 65) / 9.8382

t = 0.8894

P-value = 0.1964 (by using t-table)

= 0.01

P-value >

So, we do not reject the null hypothesis that mean amount of money spent by all customers at this supermarket is $65.

There is insufficient evidence to conclude that mean amount of money spent by all customers at this supermarket is higher than $65.

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