Answered

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Past data indicate that the amount of money contributed by the working residents of a large city to a volunteer rescue squad is a normal random variable with a standard deviation of $1.40. It has been suggested that the contributions to the rescue squad from just the employees of the sanitation department are much more variable. If the contributions of a random sample of 12 employees from the sanitation department have a standard deviation of $1.75, can we conclude at the 0.01 level of significance that the standard deviation of the contributions of all sanitation workers is greater than that of all workers living in the city?

Sagot :

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Answer:

We fail to reject the Null and conclude that the standard deviation of the contributions of all sanitation workers is not greater than that of all workers living in the city.

Step-by-step explanation:

σ = 1.40 ; σ² = 1.40² = 1.96

H0 : σ² = 1.96

H0 : σ² > 1.96

Given that:

Sample size, n = 12

Population Standard deviation, σ = 1.40

Sample standard deviation, s = 1.75

α = 0.01

The test statistic :

χ² = [(n-1)s²] ÷ σ²

χ² = [(12 - 1) * 1.75²] ÷ 1.40²

χ² = (11 * 3.0625) ÷ 1.96

χ² = 33.6875 / 1.96

χ² = 17.1875

χ² = 17.19

Using the Pvalue from Chisquare score calculator;

df = n - 1 ; 12 - 1 = 11

Pvalue ; χ²(17.19, 11) = 0.10238

Since Pvalue > α ; We fail to reject the Null and conclude that the standard deviation of the contributions of all sanitation workers is not greater than that of all workers living in the city.

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