Question

The resting pulse rate of a simple random sample of 9 women was recorded yielding a mean resting pulse rate of 76 beats per minute with standard deviation 5. Use this information for this question and the next one. The p-value of a statistical test where the alternative hypothesis is that the mean resting pulse rate is greater than 72 is:
(a) Between 0 and 0.01
(b) Between 0.01 and 0.025
(c) Between 0.025 and 0.05
(d) Between 0.05 and 0.1
(e) Greater than 0.1
The resting pulse rate of a simple random sample of 9 women was recorded yielding a mean resting pulse rate of 76 beats per minute with standard deviation 5. What is a 95% confidence interval for the mean resting pulse rate?
(a) [72.16;79.84]
(b) [72.73;79.27]
(c) [72.9;79.1]
(d) [73.26;78.74]
(e) None of the above.

Answer 1

Solution:
Part i) The resting pulse rate of a simple random sample of 9 women was recorded yielding a mean resting pulse rate of 76 beats per minute with standard deviation 5.

Sample size = n = 9

Sample mean =

Sample standard deviation= s = 5

we have to find the p-value of a statistical test where the alternative hypothesis is that the mean resting pulse rate is greater than 72 .

Thus this means this is one tailed ( Right tailed ) test.

First find t test statistic:

df = n - 1 = 9 - 1 = 8

Look in t table for df = 8 row and find the interval in which t = 2.400 fall.

then find corresponding one tail area.

t = 2.400 fall in between 2.306 and 2.896

Thus corresponding one tail area is between 0.01 to 0.025

Thus option b) Between 0.01 and 0.025 is correct.

Part ii) Find a 95% confidence interval for the mean resting pulse rate

where

t_c is t critical value for df = 8 and two tail area = 1 - c = 1 - 0.95 = 0.05

From t table t_c = 2.306

Thus

Thus

Thus option a) [72.16;79.84] is correct