Question

A type of golf ball is tested by dropping it onto a hard surface from a height of 1 meter. The height it bounces is known to be normally distributed. A sample of 25 balls is tested and the bounce heights are given below. Use Excel to find a 95% confidence interval for the mean bounce height of the golf ball. Round your answers to two decimal places and use increasing order.

Height
81.4
80.8
84.4
85.6
82.9
76.0
80.0
83.2
80.8
79.6
82.9
83.4
82.2
86.0
76.2
84.8
82.0
76.3
77.0
75.4
82.0
79.8
80.4
86.9
82.1

Answer 1

Answer: (79.95, 82.61)

Explanation:

Use Excel to calculate the 95% confidence interval, where α=0.05 and n=25.

1. Open Excel and enter the given data in column A. Find the sample mean, x¯, using the AVERAGE function and the sample standard deviation, s, using the STDEV.S function. Thus, the sample mean, rounded to two decimal places, is 81.28 and the sample standard deviation, rounded to two decimal places, is 3.23.

2. Click on any empty cell, enter =CONFIDENCE.T(0.05,3.23,25), and press ENTER.

3. The margin of error, rounded to two decimal places, is 1.33. The confidence interval for the population mean has a lower limit of 81.28−1.33=79.95 and an upper limit of 81.28+1.33=82.61.

Thus, the 95% confidence interval for the mean bounce height of the golf balls is (79.95, 82.61).

Answer 2

79.95, 82.62

Explanation:

using excel to find a 95% confidence interval for the mean bounce height of the golf ball

Heights given are :

81.4

80.8

84.4

85.6

82.9

76.0

80.0

83.2

80.8

79.6

82.9

83.4

82.2

86.0

76.2

84.8

82.0

76.3

77.0

75.4

82.0

79.8

80.4

86.9

82.1

The statistical out put of the problem after solving with excel is attached below

therefore the 95% confidence interval from the attached solution will be ( 79.95, 82.62 )