Question

University personnel are concerned about the sleeping habits of students and the negative impact on academic performance. In a random sample of 377 U.S. college students, 209 students reported experiencing excessive daytime sleepiness (EDS). Is there sufficient evidence to conclude that more than half of U.S. college students experience EDS? Use a 5% level of significance.

Answer 1

Answer: The claim is false.

Explanation:

Since we have given that

n = 377

x = 209

We will use one sample proportion test:

As we know that

`\hat{p}=(x)/(n)=(209)/(377)=0.55`

Since we need to check whether more than half of U.S. college students experience EDS.

So, hypothesis are as follows:

`H_0:p\leq 0.5\\\\H_1:p>0.5`

So, it becomes

`test\ statistic=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\test\ statistic=\frac{0.55-0.5}{\sqrt{(0.5(1-0.5))/(377)}}\\test\ statistic=1.94`

According to z-table, we get that

P-value = 0.9738

As we can see that

0.97>0.05

So, we accept the null hypothesis.

Hence, the claim is false.