Question

A new small business wants to know if its current radio advertising is effective. The owners decide to look at the mean number of customers who make a purchase in the store on days immediately following days when the radio ads are played as compared to the mean for those days following days when no radio advertisements are played. They found that for 14 days following no advertisements, the mean was 17.9 purchasing customers with a standard deviation of 1.7 customers. On 10 days following advertising, the mean was 18.7 purchasing customers with a standard deviation of 1.3 customers. Test the claim, at the 0.05 level, that the mean number of customers who make a purchase in the store is lower for days following no advertising compared to days following advertising. Assume that both populations are approximately normal and that the population variances are equal.

Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.

Answer 1

The value of the test statistic used to test the effectiveness of the radio advertising by comparing the mean number of customers on advertisement days versus no advertisement days, assuming equal variances, is -1.306.

Step-by-step explanation:

To compute the value of the test statistic for testing the claim that the mean number of customers who make a purchase in the store is lower on days following no advertising compared to days following advertising, we need to use the two-sample t-test for means of two independent samples assuming equal variances.

The formula for the test statistic (t) is:

t = (X1 - X2) / sqrt[(s1^2/n1) + (s2^2/n2)]

where:

• X1 is the mean of the first sample (no advertisement days), which is 17.9,
• X2 is the mean of the second sample (advertisement days), which is 18.7,
• s1 is the standard deviation of the first sample, which is 1.7,
• s2 is the standard deviation of the second sample, which is 1.3,
• n1 is the sample size of the first sample, which is 14, and
• n2 is the sample size of the second sample, which is 10.

Plugging the values into the formula, we get:

t = (17.9 - 18.7) / sqrt[(1.7^2/14) + (1.3^2/10)]
t = -0.8 / sqrt[(2.89/14) + (1.69/10)]
t = -0.8 / sqrt[0.2064 + 0.169]
t = -0.8 / sqrt[0.3754]
t = -0.8 / 0.6127
t = -1.306

The computed t value, rounded to three decimal places, is -1.306.