Students at a high school are asked to evaluate their experience in the class at the end of each school year. The courses are evaluated on a 1-4 scale – with 4 being the best experience possible. In the History Department, the courses typically are evaluated at 10% 1’s, 15% 2’s, 34% 3’s, and 41% 4’s. Mr. Goodman sets a goal to outscore these numbers. At the end of the year he takes a random sample of his evaluations and finds 11 1’s, 14 2’s, 47 3’s, and 53 4’s. At the 0.05 level of significance, can Mr. Goodman claim that his evaluations are significantly different than the History Department’s? Hypotheses: H0: There is in Mr. Goodman’s evaluations and the History Department’s. H1: There is in Mr. Goodman’s evaluations and the History Department’s. Enter the test statistic - round to 4 decimal places. Enter the p-value - round to 4 decimal places. Can it be concluded that there is a statistically significant difference in Mr. Goodman’s evaluations and the History Department’s?

Respuesta :

There is no statistically significant difference between Mr. Goodman’s evaluations and the History Department’s as we fail to reject the null hypothesis and value of p in which p-value = 0.5893.

H0: There is no difference in Mr. Goodman’s evaluations and the History Department’s

H- There is a significant difference between Mr. Goodman’s evaluations and the History Department’s

Applying the chi-square test:

            relative  observed  expected        residual                      Chisquare

Cat frequency(p) Oi        Ei=total x p  R2i=(Oi-Ei)/√Ei    R2i=(Oi-Ei)2/Ei

1's         0.100          11.000        12.500           -0.42                         0.180

2's        0.150         14.000         18.750           -1.10                         1.203

3's       0.340         47.000       42.500            0.69                       0.476

4's       0.410          53.000       51.250            0.24                         0.060

total     1.000         125              125                                               1.9196

Through the attached file as well as shown above we get the value of X2 equal to 1.9196.

Test statistic X2 = 1.9196.

P value through Chi-Square Distribution table = 0.5893

No, it can't be concluded that there is a statistically significant difference between Mr. Goodman’s evaluations and the History Department’s as we fail to reject the null hypothesis.

To learn more about the chi-square test visit: https://brainly.com/question/14082240

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