A group of 20 students spend between 0 and 6 hours studying for an exam. How does the number of hours spent studying affect the probability that the student will pass the exam? The table below shows the number of hours each student spent studying, and whether they passed (1) or failed (0).

```

Hours 0.50 0.75 1.00 1.25 1.50 1.75 1.75 2.00 2.25 2.50

Pass 0 0 0 0 0 0 1 0 1 0

Hours 2.75 3.00 3.25 3.50 4.00 4.25 4.50 4.75 5.00 5.50

Pass 1 0 1 0 1 1 1 1 1 1

```

1. Using logistic regression, model the effect of the hours of studying on the probability of passing an exam. Interpret the model fit.

2. Calculate the predicted probability of passing the exam when a student spent 4.50 hours studying for an exam.

3. At how many hours of study does the predicted probability equal 0.5?

4. Interpret the effect of the hours spent on the odds of passing an exam.

5. Test the null hypothesis that study for exam has no effect, at $\alpha=0.10$.

A group of 20 students spend between 0 and 6 hours studying for an exam. How does the number of hours spent studying affect the probability that the student will pass the exam? The table below shows the number of hours each student spent studying, and whether they passed (1) or failed (0). \\\\\\ Hours 0.50 0.75 1.00 1.25 1.50 1.75 1.75 2.00 2.25 2.50 Pass 0 0 0 0 0 0 1 0 1 0 Hours 2.75 3.00 3.25 3.50 4.00 4.25 4.50 4.75 5.00 5.50 Pass 1 0 1 0 1 1 1 1 1 1 1. Using logistic regression, model the effect of the hours of studying on the probability of passing an exam. Interpret the model fit. 2. Calculate the predicted probability of passing the exam when a student spent 4.50 hours studying for an exam. 3. At how many hours of study does the predicted probability equal 0.5? 4. Interpret the effect of the hours spent on the odds of passing an exam. 5. Test the null hypothesis that study for exam has no effect, at $\\alpha=0.l0$