Question

Filling boxes with consistent amounts of its cereals is critical to General Mills's success. The filling variance for boxes of Count Chocula cereal is designed to be 0.02 ounces² or less. A sample of 31 boxes of Count Chocula shows a sample standard deviation of 0.16 ounces. Use α = 0.05 to determine whether the variance in the cereal box fillings is exceeding the design specification.

A) State the null and alternative hypotheses.

a) H₀: σ² = 0.02

H_a: σ² ≠ 0.02

b) H₀: σ² < 0.02

H_a: σ² ≥ 0.02

c) H₀: σ² ≥ 0.02

H_a: σ² < 0.02

d) H₀: σ² ≤ 0.02

H_a: σ² > 0.02

e) H₀: σ² > 0.02

H_a: σ² ≤ 0.02

B) Find the value of the test statistic.

test statistic=

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. The population variance does appear to be exceeding the standard.

Reject H₀. The population variance does not appear to be exceeding the standard.    

Do not reject H₀. The population variance does appear to be exceeding the standard.

Do not reject H₀. The population variance does not appear to be exceeding the standard

Answer 1

A) The Null hypotheses are:

d)

H₀: σ² ≤ 0.02

H_a: σ² > 0.02

B)Test Statistic:

p-value;

P-value is computed using the chi-square table shown below as:

The P-Value is 0.1397

C) Conclusion:

Since P-value >>0.05 hence, Do not reject H₀. The population variance does not appear to be exceeding the standard