Question

The price of a molasses crop is determined by percent of sugar in the molasses. An independent laboratory assays each crop for its sugar content and a price is agreed upon based on the results. An analyst is interested in investigating this relationship. The following data are known:

            Price (cents/pound) 25 35 45 55 65 75 85
            Percent sugar              50 54 60 68 78 82 84

Based on your answers to Questions 10 and 11 above your decision is to ______________ H₀.

Answer 1

First we find the correlation coefficient

The correlation coefficient is 0.9868, this means there is very strong positive linear relationship between price and sugar percent.

Hypothesis Testing

Null Hypothesis

Alternative Hypothesis

Under H0, the test statistic is

Degrees of freedom = n-2 = 5

The critical value of t for 5 df at 5% significance level is 2.571

Since test statistic is greater than critical value. Reject H0.

Hence there is linear relationship between price and sugar percent.