Question

Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3​ inches, with a standard deviation of

2.4 inches. A baseball analyst wonders whether the standard deviation of heights of​ major-league baseball players is less than

2.4 inches. The heights​ (in inches) of 20 randomly selected players are shown in the table.

72

74

71

73

76

70

77

76

72

72

77

72

75

70

73

74

75

73

74

74

Test the notion at the α=0.01 level of significance.

1. What are the null and alternative​ hypotheses?
2. Calculate the value of the test statistic.
3. Use technology to determine the​ P-value for the test statistic.
4. What is the correct conclusion at the α=0.01 level of​ significance?

Answer 1

using minitab

enter data>stat>basic stat>1 variance

a)

Test

Null hypothesis   H₀: σ = 2.4
Alternative hypothesis   H₁: σ < 2.4

b)Chi-Square test statistic = 14.4097  

c)p value = 0.2407

d) failed to reject H0,There is insufficient evidence to support the claim