A marketing expert for mobile operating system believes that 40% of the users prefer android. If 9 out of 20 choose android over IOS, what can you conclude about the marketing expert’s claim? Use 5% level of significance.
To test the marketing expert's claim, we can use a hypothesis test with the following hypotheses:
Null hypothesis (H0): The proportion of users who prefer Android is equal to 40%.
Alternative hypothesis (Ha): The proportion of users who prefer Android is not equal to 40%.
Let's assume that the number of users who choose Android follows a binomial distribution with n = 20 trials and a success probability of p = 0.4.
To test the claim, we will calculate the test statistic, which is the Z-score, using the formula:
Z = (p̂ - p) / √(p(1-p)/n)
Where p̂ is the proportion of users who choose Android in our sample.
Given that 9 out of 20 users choose Android, the sample proportion is p̂ = 9/20 = 0.45.
Plugging in the values, we get:
Z = (0.45 - 0.4) / √(0.4(1-0.4)/20)
= 0.05 / √(0.24/20)
= 0.05 / √0.012
= 0.05 / 0.1095
≈ 0.456
Next, we need to find the critical value for a two-tailed test with a 5% level of significance. Looking up the critical value in a standard normal table, we find it to be approximately ±1.96.
If the absolute value of the test statistic (0.456) is less than the critical value (1.96), we fail to reject the null hypothesis. If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis.
Since |0.456| < 1.96, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the proportion of users who prefer Android is different from 40%.
Therefore, based on the given data, we cannot reject the marketing expert's claim that 40% of the users prefer Android at a 5% level of significance.