Within science PhDs, is there an association between gender and pursuing a mathematics PhD? MIT recorded enrollment for the Fall term of the 2015-2016 school year. The contingency table below shows the gender and field of study for doctoral students in MIT's School of Science.
Mathematics Other Field Row Total
Women 23 367 390
Other Gender 101 639 740
Column Total 124 1006 1130
Find the test statistic and conclusion for the Test of Independence at the 1% significance level. Use the table below for the critical value. (Use expected frequencies rounded to the nearest whole number.)
Select the correct answer below:
The test statistic ̇̄̄̄ = 4.8.
Because the test statistic is less than the critical value, we do not reject the null hypothesis.
The test statistic ̇̄̄̄ = 4.8.
Because the test statistic is less than the critical value, we reject the null hypothesis.
The test statistic ̇̄̄̄ = 4.8.
Because the test statistic is greater than the critical value, we reject the null hypothesis.
The test statistic ̇̄̄̄ = 16.0.
Because the test statistic is greater than the critical value, we reject the null hypothesis.
The test statistic ̇̄̄̄ = 16.0.
Because the test statistic is greater than the critical value, we do not reject the null hypothesis.
The test statistic ̇̄̄̄ = 16.0.
Because the test statistic is less than the critical value, we reject the null hypothesis.
df ̇̄̄̄_0.10 ̇̄̄̄_0.05 ̇̄̄̄_0.025 ̇̄̄̄_0.01 ̇̄̄̄_0.005
1 2.706 3.841 5.024 6.635 7.879
2 4.605 5.991 7.378 9.210 10.597
3 6.251 7.815 9.348 11.345 12.838
4 7.779 9.488 11.143 13.277 14.860