Question

A large candy manufacturer in Slidell produces, packages, and sells packs of candy targeted to weigh 500 grams. The weight of a pack of candy is normally distributed with the mean μ=500 grams, but Parker Sanderson, a quality control manager working for the company, was concerned that the variation in the actual weights of the targeted 500-gram packs was larger than acceptable. That is, he was concerned that some packs weighed significantly less than 500-grams and some weighed significantly more than 500 grams. In an attempt to estimate σ, the standard deviation of the weights of all of the 500-gram packs the manufacturer makes, he took a random sample of n = 24 packs off of the factory line. The random sample yielded a sample standard deviation of 23.6 grams.

(1) Construct a 95% confidence interval of the unknown population standard deviation σ.

(2) Test the alternate hypothesis that the population standard deviation σ is significantly larger than 20 grams.

(i) Alternatives

Select one:

H₀: σ ≤ 20                    H₁: σ > 20

H₀: σ² ≤ 20 H₁: σ² > 20

H₀: σ ≥ 20                    H₁: σ < 20

H₀: σ = 20                    H₁: σ ≠ 20

None of the other four

(ii) Test statistic

Select one:

χ* = 5.66

χ* = 24.71

χ* = 32.03

χ* = 43.21

None of the other four

(iii) p-value

Select one:

Approximately 0.01

Approximately 0.05

Approximately 0.10

Approximately 0.20

Approximately 0.025

(iv) What is the conclusion if the level of significance is α=0.05?

Select one:

Conclude H₀ that the population standard deviation σ is larger than 20 grams.

Conclude H₀ that the population standard deviation σ is no larger than 20 grams.

Conclude H₁ that the population standard deviation σ is larger than 20 grams.

Conclude H₁ that the population standard deviation σ is no larger than 20 grams.

None of the other four

Answer 1

1)

The 95% confidence interval is 336.4378 $< \sigma^2 <$ 1095.951

2)

hypothesis

A) H₀: σ ≤ 20                    H₁: σ > 20

TS = 32.03

p-value = 0.0996

Approximately 0.10

we fail to reject the null hypothesis

Conclude H₀ that the population standard deviation σ is no larger than 20 grams.