Question

1. A new program is developed to increase the overall number of runs for Major League Baseball teams by an outside sporting company, Run Boys Run. In 2015, the average number of runs scored for the entire season by a sample of 25 teams is 690.24. The population standard deviation is 58.36.

1. Find the standard error.

2. Identify the upper and lower z score for a 95% confidence interval for µ.

3. Calculate the upper and lower bounds of the confidence interval.

Answer 1

Solution :

Given that,

= 690.24

= 58.36.

n = 25

A ) The standard error = (/n)

= (58.36./ 25 )

= 11.67

   The standard error = 11.67

B ) At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = E = Z_/2* (/n)

= 1.960 * (58.36./ 25 )

= 22.88

Margin of error = E = 22.80

At 95% confidence interval estimate of the population mean is,

- E < < + E

690.24 - 22.88 < < 690.24 + 22.88

667.36 < < 713.12

C ) The upper bounds = 713.12

The lower bounds = 667.36