Question

A major credit card company is interested in the proportion of individuals who use a competitor's credit card. Their null hypothesis is H₀:p=0.65, and based on a sample, they find a sample proportion of 0.70 and a p-value of 0.053. Is there convincing statistical evidence at the 0.05 level of significance that the true proportion of individuals who use the competitor's card is actually greater than 0.65?

a) No, because the p-value 0.053 is greater than the significance level 0.05
b) Yes, because the p-value 0.053 is less than the significance level 0.05
c) Yes, because the sample proportion is greater than the null hypothesis proportion
d) No, because the sample proportion is not significantly different from the null hypothesis proportion

Answer 1

No, because the p-value 0.053 is greater than the significance level 0.05

Step-by-step explanation:

The null hypothesis states that the true proportion of individuals who use the competitor's credit card is 0.65. The sample proportion is 0.70, and the p-value is 0.053. To determine if there is convincing statistical evidence that the true proportion is actually greater than 0.65, we compare the p-value to the significance level.

The significance level is given as 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is true). If the p-value is less than the significance level, we reject the null hypothesis. In this case, the p-value (0.053) is greater than the significance level (0.05), so we do not have convincing statistical evidence to conclude that the true proportion is greater than 0.65.

Therefore, the correct answer is:

a) No, because the p-value 0.053 is greater than the significance level 0.05