Question

In: Statistics and Probability

In the 1920's about 97% of US colleges and universities required a physical education course for...

In the 1920's about 97% of US colleges and universities required a physical education course for graduation. Today, about 40% require such a course. A recent study of physical education requirements included 354 institutions: 132 private and 222 public. Among the private institutions, 100 required a physical education course, while among the public institutions, 61 required a course.

a) what are the statistics (+/- 0.0001)?

X1=?, n1=?, p1=?

X2=?, n2=?, p2=?

b) use a 95% confidence interval to compare the private and public institutions with regard to the physical education requirement (+/- 0.0001)

The 95% confidence interval is from ---- to ----

Conclusion:

We have evidence to conclude that private institutions are more likely to require physical education

OR

We have no evidence to conclude that private institutions are more likely to require physical education

c) Use a significance test to compare the private and the public institutions with regard to the physical education requirement (+/- 0.0001)

p=?

z=?

P-value=?

Conclusion

We have no evidence to conclude that public institutions are more likely to require physical education

OR

We have evidence to conclude that public institutions are more likely to require physical education

Solutions

Expert Solution

a)

b)

The 95% Confidence Interval of the difference of two proportions is obtained using the formula,

Where,

For 95% confidence interval, z critical value is obtained using the standard normal distribution table,

Conclusion:

We have evidence to conclude that private institutions are more likely to require physical education

Explanation: Since the confidence interval for the difference is proportions is significantly larger we can conclude that private institutions are more likely to require physical education

c)

The pooled proportion is obtained using the formula,

The z-statistic is,

The P-value for the z-statistic is obtained from z distribution table for z = 8.8215

Conclusion

We have no evidence to conclude that public institutions are more likely to require physical education

Explanation:

Since the p-value is less than 0.05 at 5% significance level, the null hypothesis is rejected. Hence there is no evidence to conclude that public institutions are more likely to require physical education


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