Question

An AP Statistics teacher claims that the AP Statistics grade distribution is as follows: Grade Percentage 5% 20% 40% 15% Suppose that a sample of 100 students taking AP Statistics class yields the observed counts shown below: Grade Number of Students 17 25 35 15 Use a 0.10 significance level to test the claimed AP Statistics grade distribution is correct (a) Identify the appropriate hypothesis test and explain the reasons why it is appropriate for analyzing this data. (b) Identify the null hypothesis and the alternative hypothesis. (c) Determine the test statistic. (Round your answer to two decimal places) (d) Determine the p-value. (Round your answer to two decimal places) (e) Compare p-value and significance level a. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why? (f Is there sufficient evidence to support that the claimed AP Statistics grade distribution is correct? Justify your answer

Answer 1

(a)

Here we need to test whether sample of students follow the distribution of AP Statistics grade so chi square goodness of test will be used.

(b)

H0: Data follows the distribution of AP Statistics grade.

Ha: Data does not follow the distribution of AP Statistics grade.

(c)

Following table shows the calculations for test statistics;

	O	p	E=p*100	(O-E)^2/E
	25	0.2	20	1.25
	35	0.4	40	0.625
	15	0.2	20	1.25
	17	0.15	15	0.26666667
	8	0.05	5	1.8
Total	100		100	5.19166667

Following is the test statistics:

$\chi^{2}=\sum \left ( \frac{(O-E)^{2}}{E} \right )=5.19$

(d)

Degree of freedom: df=n-1=4

The p-value using excel function "=CHIDIST(5.19,4)" is: 0.2684

(e)

Since p-value is greater than level of significance 0.05 so we fail to reject the null hypothesis.

(f)

There is evidence to conclude that AP Statistics grade.distribution is correct.