Question

Your psychology teacher claims that 31 percent of students pass his course. You think his claim is too high. Use the 0.01 alpha level.

You sample 435 students and find 122 of them passed the course.

What is the test statistic? (Report answer accurate to three decimal places.)


What is the p-value? (Report answer accurate to four decimal places.)


The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• At the 0.01 alpha level, I was unable to show that the percentage of students passing the course was significantly less than 31 percent.
• At the 0.01 alpha level, I was unable to show that the percentage of students passing the course was significantly greater than 31 percent.
• At the 0.01 alpha level, I was unable to show that the percentage of students passing the course was significantly different than 31 percent.
• At the 0.01 alpha level, I was able to show that the percentage of students passing the course was significantly less than 31 percent
• At the 0.01 alpha level, I was able to show that the percentage of students passing the course was significantly greater than 31 percent
• At the 0.01 alpha level, I was able to show that the percentage of students passing the course was equal to 31 percent

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.31

Ha : p < 0.31

n = 435

x = 122

= x / n = 122 / 435 =0.28

P0 = 0.31

1 - P0 = 1 - 0.31 =0.69

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.28-0.31/ [(0.31*0.69) / 435]

= -0.13

Test statistic = z = -0.13

P(z < -0.13) = 0.4483

P-value = 0.4483

= 0.01

P-value <

0.4483 > 0.01

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that

At the 0.01 alpha level, I was unable to show that the percentage of students passing the course was significantly less than 31 percent.