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 2.8 inches. A baseball analyst wonders whether the standard deviation of heights of​ major-league baseball players is less than 2.8 inches. The heights​ (in inches) of 20 randomly selected players are shown in the table.

Answer 1

Solution:-

Mean = 69.3, S.D = 2.8

n = 20

72	74	71	72	76
70	77	75	72	72
77	72	75	70	73
74	75	73	74	74

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H₀: σ > 2.80

Alternative hypothesis H_A: σ < 2.80

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (X²).

DF = n - 1 = 20 -1

D.F = 19

$\chi ^{2}=\frac{(n-1)s^{2}}{\sigma ^{2}_{0}}$

$\chi ^{2}=\frac{(20-1)\times (2.062)^{2}}{(2.8)^2}$

X² = 10.304

We use the Chi-Square Distribution Calculator to find P(Χ² < 10.304) = 0.055

Interpret results. Since the P-value (0.055) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that standard deviation of heights of​ major-league baseball players is less than 2.8 inches.