Question

In 2010, 76.3% of college students enrolled in an education major were female. A sample of students enrolled in an education major in 2019 consisted of 115 females and 70 males.

Would this data be sufficient at the 0.01 level of significance to conclude that the percentage of females enrolled in an education major decreased from the 76.3%?

Use the P-Value Method of Testing.

In your work space below, you will need to have -
1. The null hypothesis, Ho
2. The alternative hypothesis, H1
3. The test statistic
4. The type of test(left, right, two-tailed) and the p-value
5. The decision to accept Ho or reject Ho

Answer 1

Solution :

Given that,

= 0.763

1 - = 0.237

n = 115

x = 70

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 0.609

1)

The null and alternative hypothesis is,

Ho: p = 0.763

20

Ha: p < 0.763

3)

Test statistics

z = ( - ) / *(1-) / n

= ( 0.609 - 0.763) / (0.763*0.237) /115

= -3.891

4)

This a left (One) tailed test.

P-value = P(Z < -3.891 )

= 0.0000

5)

The p-value is p = 0.0, and since p = 0. < 0.01, it is concluded that the null hypothesis is rejected.

Reject H0.