The mean weekly sales of a four-wheeler were 50 units per agency in 20 agencies. After an advertising campaign, the mean weekly sales increased to 55 units per agency with standard deviation of 10 units. Test whether the advertising campaign was successful. (Use $t_{0.005} = 1.729$ for $19 d.f.$)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Yes, the campaign was successful; the increase in sales is statistically significant.
Given $μ_0 = 50, \bar x = 55, s = 10, n = 20$
$⇒ d.f. = 20-1= 19$
As we know that $t =\frac{\bar x - μ_0}{\frac{s}{\sqrt{n}}}=\frac{55-50}{\frac{10}{\sqrt{20}}}=2.236$
Let the hypothesis be given as
null hypothesis $H_0: μ_0=50$
Alternative hypothesis $H_a: μ_0> 50$
Given that $t_{d. f (α)} = t_{19 (0.05)} = 1.729$
We have calculated t = 2.236
$∵t> t_α$, so null hypothesis is rejected.
Hence, advertising campaign was successful.