Hydrangea is a flower that changes its color according the the pH of the soil. The flower becomes blue when the pH of the soil is too acidic (pH below 5.5), red when the pH of the soil is too basic (pH above 6.5), and purple when the pH of the soil is exactly between 5.5 to 6.5. A landowner claims that the average pH of their soil can produce perfectly consistent purple flowers with a standard deviation pH of at most 0.5. A flower cultivator thinks the standard deviation of the pH of the soil may be greater than 0.5, so they tested 15 random sites from the land area. Use a level of significance of α = 0.05. 1) This problem is a test on what population parameter? a. Mean b. Variance / Standard Deviation c. Population Parameter 2) What is the null and alternative hypothesis? a. The standard deviation of the soil's pH IS EQUAL TO 0.5 (Ho: θ = 0.5); The standard deviation of the soil's pH DOES NOT EXCEED 0.5 (Ho: θ < 0.5) b. The standard deviation of the soil's pH IS EQUAL TO 0.5 (Ho: θ = 0.5); The standard deviation of the soil's pH EXCEEDS 0.5 (Ho: θ > 0.5) c. The standard deviation of the soil's pH IS EQUAL TO 0.5 (Ho: θ = 0.5); The standard deviation of the soil's pH IS NOT EQUAL TO (Ho: θ ≠ 0.5) 3) What is the type of test? a. Right-tailed b. Left-tailed c. Two-tailed 4) Statistical Decision a. With 0.05 level of significance, there is enough evidence to indicate that the standard deviation of the soil's pH exceed 0.5, making the color of the flowers inconsistent. b. With 0.05 level of significance, there is no sufficient evidence to indicate that the standard deviation of the soil's pH exceed 0.5, making the color of the flowers consistent enough.
Hydrangea is a flower that changes its color according the the pH of the soil. The flower becomes blue when the pH of the soil is too acidic (pH below 5.5), red when the pH of the soil is too basic (pH above 6.5), and purple when the pH of the soil is exactly between 5.5 to 6.5. A landowner claims that the average pH of their soil can produce perfectly consistent purple flowers with a standard deviation pH of at most 0.5.
A flower cultivator thinks the standard deviation of the pH of the soil may be greater than 0.5, so they tested 15 random sites from the land area. Use a level of significance of α = 0.05.
1) This problem is a test on what population parameter?
a. Mean
b. Variance / Standard Deviation
c. Population Parameter
2) What is the null and alternative hypothesis?
a. The standard deviation of the soil's pH IS EQUAL TO 0.5 (Ho: θ = 0.5); The standard deviation of the soil's pH DOES NOT EXCEED 0.5 (Ho: θ < 0.5)
b. The standard deviation of the soil's pH IS EQUAL TO 0.5 (Ho: θ = 0.5); The standard deviation of the soil's pH EXCEEDS 0.5 (Ho: θ > 0.5)
c. The standard deviation of the soil's pH IS EQUAL TO 0.5 (Ho: θ = 0.5); The standard deviation of the soil's pH IS NOT EQUAL TO (Ho: θ ≠ 0.5)
3) What is the type of test?
a. Right-tailed
b. Left-tailed
c. Two-tailed
4) Statistical Decision
a. With 0.05 level of significance, there is enough evidence to indicate that the standard deviation of the soil's pH exceed 0.5, making the color of the flowers inconsistent.
b. With 0.05 level of significance, there is no sufficient evidence to indicate that the standard deviation of the soil's pH exceed 0.5, making the color of the flowers consistent enough.
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