The following table lists the sugar content of two types of apples from three different orchards. At $= .05$, test the claim that the sugar content of the apples and the orchard where they were grown are not related . $\begin{array}{lccc} \text { Sugar Content } & \text { Orchard 1 } & \text { Orchard 2 } & \text { Orchard } 3 \ \text { Apple Type 1 } & 3 & 2 & 3 \ \text { Apple Type 2 } & 23 & 10 & 3 \end{array}$ A)There is evidence to reject the claim that the sugar content of the apple type and the orchard number are . not related because the test value $5.991 4.873$ B)There is not evidence to reject the claim that the sugar content of the apple type and the orchard number . are not related because the test value $4.873 2.687$ D)There is not evidence to reject the claim that the sugar content of the apple type and the orchard number . are not related because the test value $2.687

Question

The following table lists the sugar content of two types of apples from three different orchards. At $= .05$, test the claim that the sugar content of the apples and the orchard where they were grown are not related . $\begin{array}{lccc} \text { Sugar Content } & \text { Orchard 1 } & \text { Orchard 2 } & \text { Orchard } 3 \ \text { Apple Type 1 } & 3 & 2 & 3 \ \text { Apple Type 2 } & 23 & 10 & 3 \end{array}$ A)There is evidence to reject the claim that the sugar content of the apple type and the orchard number are . not related because the test value $5.991 > 4.873$ B)There is not evidence to reject the claim that the sugar content of the apple type and the orchard number . are not related because the test value $4.873 < 5.991$ C)There is evidence to reject the claim that the sugar content of the apple type and the orchard number are . not related because the test value $12.592 > 2.687$ D)There is not evidence to reject the claim that the sugar content of the apple type and the orchard number . are not related because the test value $2.687 < 12.592$

Quizplus · Accepted Answer

To test the claim that the sugar content of the apples and the orchard where they were grown are not related, we need to perform a chi-square test of independence. Using the given data, we calculate the expected frequencies assuming independence and then find the chi-square test statistic. The degrees of freedom for the test is $(r-1)(c-1) = (2-1)(3-1) = 2$, where $r$ is the number of rows and $c$ is the number of columns in the table.

Performing the calculation, we get a test value of $\chi^2 = 4.873$. The critical value for a chi-square distribution with 2 degrees of freedom at $\alpha = .05$ is 5.991. Since $4.873 < 5.991$, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the sugar content of the apple type and the orchard number are related. Hence, the best choice is B which states that there is not evidence to reject the claim.

The Following Table Lists the Sugar Content of Two Types =.05= .05=.05

The Following Table Lists the Sugar Content of Two Types $= .05$