Question

I need the answer to the following, but not using the P value.

1. A telephone company claims that less than 15% of all college students have their own cell phone plan. A random sample of 70 students revealed that 8 of them had their own plan. Test the company's claim at the 0.05 level of significance.

2. A college statistics instructor claims that the mean age of college statistics students at a local Dallas-based institution is 23. A random sample of 35 college statistics students revealed a mean age of 25.1. The population standard deviation is known to be 4.1 years. Test his claim at the 0.1 level of significance.

3. A random sample of 85 adults ages 18-24 showed that 11 had donated blood within the past year, while a random sample of 254 adults who were at least 25 years old had 18 people who had donated blood within the past year. At the 0.05 level of significance, test the claim that the proportion of blood donors is not equal for these two age groups.

Answer 1

1. Here claim is that p<0.15

So vs

Now

So test statistics is

The z-critical value for a left-tailed test, for a significance level of α=0.05 is

zc​=−1.64

Graphically

As test statistics do not fall in the rejection region we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that p<0.15