Question

5. In January 2005, a company that monitors Internet traffic (WebSideStory) reported that its sampling revealed that the Mozilla Firefox browser launched in 2004 had grabbed a 4.6% share of the market. I. If the sample were based on 2,000 users, could Microsoft conclude that Mozilla has a less than 5% share of the market? II. WebSideStory claims that its sample includes all the daily Internet users. If that’s the case, then can Microsoft conclude that Mozilla has a less than 5% share of the market?

Answer 1

(I) We conclude that Mozilla has more than or equal to 5% share of the market.

(II) Yes, we can conclude that Mozilla has a less than 5% share of the market.

Step-by-step explanation:

We are given that in January 2005, a company that monitors Internet traffic (WebSideStory) reported that its sampling revealed that the Mozilla Firefox browser launched in 2004 had grabbed a 4.6% share of the market.

(I) Let p = population proportion share of the market by Mozilla

So, Null Hypothesis, $H_0$ : p $\geq$ 5%      {means that Mozilla has more than or equal to 5% share of the market}

Alternate Hypothesis, $H_A$ : p < 5%       {means that Mozilla has a less than 5% share of the market}

The test statistics that will be used here is One-sample z-test for proportions;

                           T.S.  =   $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$  ~ N(0,1)

where, $\hat p$ = sample proportion of the share of the market grabbed by Mozilla in 2004 = 4.6%

           n = sample of users = 2,000

So, the test statistics =  $\frac{0.046-0.05}{\sqrt{\frac{0.05(1-0.05)}{2,000} } }$

                                    =  -0.821

The value of z-test statistics is -0.821.

Since in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% level of significance the z table gives a critical value of -1.96 for left-tailed test.

Since the value of our test statistics is more than the critical value of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that Mozilla has more than or equal to 5% share of the market.

(II) We are given that WebSideStory claims that its sample includes all the daily Internet users. This means that the 4.6% share of the market represents the whole population.

Hence, we can conclude that Mozilla has a less than 5% share of the market.