Question

Suppose that you sample 28 high school baseball pitchers in one country and find that they have a mean fastball pitching speed of 80.5mph with a standard deviation of 5.2 mph.

a. find a point estimate for the mean fastball pitching speed of all high school baseball pitchers in the country.

b. find a 99% confidence interval for the mean fastball pitching speed of all high school baseball pitchers in the country.

n=

x bar=

s or sigma value=

z or t value=

df (of none, type NA=

error=

LCL=

UCL=

Answer 1

Here, the sample size , n = 28

the sample mean , = 80.5

sample standard deviation , s = 5.2

a) a point estimate for the mean fastball pitching speed of all high school baseball pitchers in the country is the sample mean.

Therefore , point estimate = 80.5

b)We have to find a 99% confidence interval.

We use the t distribution.

Degrees of freedom = n - 1 = 27

Using the t critical values table, at 99% confidence level and df = 27 , the critical value is , t = 2.77

The confidence interval is = t*s/n

= 80.5 2.77 * 0.98

= 80.5 2.723

= (77.78 , 83.22)

LCL = 77.78

UCL = 83.22

error = 2.723