Question

pH is a measure of acidity that winemakers must watch. A "healthy wine" should have a pH in the range 3.1 to 3.7. The target standard deviation is σ = 0.50 (i.e., σ² = 0.25). The pH measurements for a sample of 16 bottles of wine are shown below. At α = .05 in a two-tailed test, is the sample variance either too high or too low?

3.48	3.54	3.27	3.46	3.45	3.46	3.33	3.60
3.46	3.55	3.54	3.43	3.50	3.35	3.28	3.56

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(a) Choose the correct null and alternative hypotheses.

1. H₀: σ² = 0.25 vs. H₁: σ² ≠ 0.25
2. H₀: σ² ≤ 0.25 vs. H₁: σ² > 0.25
3. H₀: σ² ≥ 0.25 vs. H₁: σ² < 0.25

• a

• b

• c

(b) Choose the correct decision rule.

1. Reject the null hypothesis if χ² > 25.00 or χ² < 7.266
2. Reject the null hypothesis if χ² < 27.49 or χ² > 6.267
3. Reject the null hypothesis if χ² > 27.49 or χ² < 6.262

• a

• b

• c

(c) Calculate χ². (Round your answer to 2 decimal places.)

χ² =

(d) Choose the correct conclusion.

1. Reject H₀. There is not enough evidence to conclude that the variance is different from 0.25.
2. Fail to reject H₀. There is significant evidence to conclude that the variance is different from 0.25.

• a

• b

Need help with step C

Answer 1