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 2.9 inches. A baseball analyst wonders whether the standard deviation of heights of​ major-league baseball players is less than 2.9 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 73 75 70 73

74 75 73 74 74

X^2= __________________ (to 3 decimals) P value is ________________ (to 3 decimals) Conclusion? __________________________________

Answer 1

Answer:

Given,

sample = 20

standard deviation =2.9

alpha = 0.10

S^2 = 4.05 [from the data given]

Now Ho : standard deviation >= 2.9

H1 : standard deviation < 2.9

Now consider the test statistics

i.e.,

= (n - 1)S^2 /standard deviation^2

= (20 - 1)*4.05/2.9^2

Test statistic = 9.150

Now p value = ?

P(test statistic < 9.150) = 0.029

P value = 0.029

Hence we conclude that the p value is less than the alpha.so we reject Ho and here we have sufficient evidence to conclude that the standard deviation is less than 2.9 at 1% significance.