Answer to Question #155998 in Statistics and Probability for Max

Question

Find the null and alternative hypothesis of the following and identify the type of hypothesis testing:

1.) It has been known that a fixed dosage of a certain medicine results to an average increase of pulse rate by at least 12 beats per minute with a standard deviation of 5. A group of 10 patients given the same dose has shown the following pulse rate increases: 15, 10, 12, 11, 9, 10, 17, 14, 15, and 7. Is there proof to show that this group has a lower average increase of pulse than the others in general?

2.) Fifty senior high school students in Statistics got an average grade of 94 with a standard deviation of 2 while another group of 60 senior high school students got an average grade of 92 with a standard deviation of 3. Can the difference in the mean grade be attributed to chance using a 0.04 level of significance?

Answer 1

1)

$H_0: \mu\ge12$

$H_a:\mu<12$

This is a left-tailed hypothesis testing for a single mean and since the population standard deviation is known we use a z-test.

2)

$H_0:\mu_1=\mu_2$

$H_a:\mu_1\ne\mu_2$

This is two-tailed hypothesis testing for the difference in the means and since sample sizes are bigger than 30 we use a z-test.