A teacher claims that, on average, 30% of students in his class get an A, 15% get a B, 15% get a C, 40% get a D and the rest get an F. The grades of a random sample of his students over the years is recorded. Test the claim at 0.05% significance.
Test for the claim that the following categories occur with the following frequencies:
pA=0.3pA=0.3; pB=0.15pB=0.15; pC=0.15pC=0.15; pD=0.4pD=0.4Test at the 0.05 significance level. Complete the table. Round all answers to three decimal places.
Category |
Observed
Frequency |
Expected
Frequency |
Residual |
|---|
A |
17 |
|
|
|---|
B |
14 |
|
|
|---|
C |
32 |
|
|
|---|
D |
40 |
|
|
|---|
HoHo : pA=0.3pA=0.3; pB=0.15pB=0.15; pC=0.15pC=0.15; pD=0.4pD=0.4
H1H1: at least one is different
Original claim = Select an answer H₁ H₀
Enter the critical value, along with the significance level and degrees of freedom χ2χ2(αα,df) below the graph. (Graph is for illustration only. No need to shade.)
(Round to three decimal places.)
Test Statistic =(Round to three decimal places.)
p-value=
(Round to four decimal places.)
Decision: Select an answer Accept the null hypothesis Reject the null hypothesis Accept the alternative hypothesis Fail to reject the null hypothesis
Conclusion: Select an answer The sample data supports There is not enough evidence to support There is sufficient evidence to warrant rejection of There is not sufficient evidence to warrant rejection of the claim that all 4 categories are equally likely to be selected.