Question

A popular blog reports that 60% of college students log into Facebook on a daily basis.
The Dean of Students at a certain university thinks that the proportion may be different at
her university. She polls a simple random sample of 200 students, and 134 of them report
that they log into Facebook daily. Can you conclude that the proportion of students who
log into Facebook daily differs from 60%? Use the α = .01 level.

a) What is the sample proportion?

b) Find the standard error.

c) Write the Hypothesis Test.

d) What kind of test?

e) Draw the bell curve relative to Ho

f) Find the z score for the answer you found in part (a).

g) Draw the p-value region on the standard bell curve.

h) Calculate the p-value.

i) What is the result using α = .05?
j) Describe in words the result of your study.

Answer 1

The sample size is N = 200

, the number of favorable cases is X = 134

, and the sample proportion is

and the significance level is α=0.01

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p = 0.6

Ha: p ≠ 0.6

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is z_c = 1.96

The rejection region for this two-tailed test is R={z:∣z∣>1.96}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that

∣z∣=2.021>zc​=1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0433,

and since p=0.0433<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is different than p0​, at the α=0.05 significance level.

Hence we conclude that the proportion of students who
log into Facebook daily differs from 60% in that particular university.

Confidence Interval

The 95% confidence interval for p is: 0.605<p<0.735.

Graphically