Question

A company has launched a new product. This company is a reputed company with 50% market share of similar range of products. The competitors also enter with their new products equivalent to your new product. Based on earlier experience you initially estimated that, your market share of the new product would be 50%. You carry out random sampling of 15 customers who have purchased the new product and realize that only four of them have actually purchased your product. Test, if you are likely to have half or more of market share at  = 0.10 (10% significance level)

Answer 1

H0: p > 0.50

H1: p < 0.50

$\widehat p$ = 4/15 = 0.267

The test statistic is

$z = \frac{\widehat p - p}{\sqrt{\frac{p(1 - p)}{n}}}$

  

0.267 – 0.5 0.5(1-0.5) 15

  $=-1.80$

At alpha = 0.10, the critical value is -z0.1 = -1.28

Since the test statistic value is less than the critical value (-1.80 < -1.28), so we should reject the null hypothesis.

At 0.10 significance level, there is sufficient evidence to conclude that we are likely to have half or more market share.