91影视

Percentage of freshman $=29\%$.

Percentage of sophomores $=27\%$.

Percentage of juniors $=25\%$.

Percentage of seniors $=19\%$.

Number of freshmen in a sample $=54$.

Number of sophomores in a sample $=66$.

Number of juniors in a sample $=56$.

Number of seniors in a sample $=30$.

Total number of students in a sample $=54+66+56+30$

$=206$.

Finding percentages:

Freshman: $\frac{54}{206}脳100=26.21\%$.

Sophomores: $\frac{66}{206}脳100=32.05\%$.

Juniors: $\frac{56}{206}脳100=27.18\%$.

Seniors: $\frac{30}{206}脳100=14.56\%$.

Graph:

For sample data

Interpretation:

The preceding graph shows that the majority of students are in the sophomores and then juniors groups, however the claimed statistic indicates that the majority of students are in the freshman group.

The school roster shows that $29\%$ of the students enrolled at the school are freshmen, $27\%$ are sophomores, $25\%$ are juniors, and $19\%$ are seniors.

The expected count will be

The observed (O) and expected (E) counts are

The null and alternate hypotheses are

$H_0:p_1=0.29,$

$p_2=0.27,$

$p_3=0.25,$

$p_4=0.19$

$H_1$: At least one of the proportions is not equal.

Test statistic

$\frac{(54-59.74{)}^2}{59.74}+\frac{(66-55.62{)}^2}{55.62}+\frac{(56-51.5{)}^2}{51.5}+\frac{(30-39.14{)}^2}{39.14}~{蠂}_3$

The test value is $5.016$.

P value

$P\left({蠂}_3>5.016\right)=0.170629$

Conclusion:

Because the p value is bigger than the significance level, there is insufficient evidence to reject the null hypothesis at the $5\%$level of significance, leading to the conclusion that the actual and sample distributions are identical, and the sample data represents the real data.