Question

As of 2012, the proportion of students who use a MacBook as their primary computer is 0.46. You believe that at your university the proportion is actually less than 0.46. The hypotheses for this scenario are Null Hypothesis: p ≥ 0.46, Alternative Hypothesis: p < 0.46. You conduct a random sample and run a hypothesis test yielding a p-value of 0.4734. What is the appropriate conclusion? Conclude at the 5% level of significance.1) We did not find enough evidence to say the proportion of students that use a MacBook as their primary computer is less than 0.46.

2) The proportion of students that use a MacBook as their primary computer is greater than or equal to 0.46.
3) We did not find enough evidence to say the proportion of students that use a MacBook as their primary computer is larger than 0.46.
4) We did not find enough evidence to say a significant difference exists between the proportion of students that use a MacBook as their primary computer and 0.46
5) The proportion of students that use a MacBook as their primary computer is significantly less than 0.46.

Answer 1

We did not find enough evidence to say the proportion of students that use a MacBook as their primary computer is less than 0.46.

Explanation:

The hypothesis :

H0 : p = 0.46

H1 : p < 0.46

Pvalue = 0.4734

Level of significance, α = 5% = 0.05

Defining the Decison region :

Using Pvalue :

If Pvalue < α ; We reject the Null, H0 otherwuse, fail to reject the Null ;

0.4734 > α ; Here, Pvalue > α ; Hence, we fail to reject the null

Hence, there is not enough evidence to conclude that proportion of students that use a MacBook as their primary computer is less than 0.46