Question

The market research group of a manufacturer of computing equipment believes that the piece of equipment people purchase is related to the highest college degree that they earned. To determine if this belief is true, the firm surveyed a sample of 600 buyers with different degrees to determine whether they purchased a desktop, laptop, or tablet computer They organized the data along two categorical variables: first, type of equipment-desktop, laptop, or tablet, second, type of degree- undergraduate or graduate. The results are given in the following table Highest Degree Undergraduate Graduate Desktop 75 120 Laptop 50 85 Tablet 175 95 The null hypothesis for the test of independence is: Ho: Preference for computer type is independent of highest degree. (True or False True e False

Answer 1

Solution:- False, Preference for computer type is not independent of highest degree.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H₀: Preference for computer type and highest degree are independent.
H_a: Preference for computer type and highest degree are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (3 - 1)
D.F = 2
E_r,c = (n_r * n_c) / n

$\chi ^{2}=\sum \left [\frac{(O_{r,c}-E_{r,c})^{2}}{E_{r,c}} \right ]$
Χ² = 43.16

Expected [(O ErErlTotal ExpectedOr-Er) ErTablet Desk 300 175 135 11.851851851851 50 67.5 4.537037037037 75 97.5 5.192307692307 Undergraduate 95 270 135 11.851851851851 270 23.703703703703 300 600 67.5 4.537037037037 Graduate Total 120 195 97.5 5.192307692307 195 10.38461538461 85 135 135 9.0740740740740

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 43.16.

We use the Chi-Square Distribution Calculator to find P(Χ² > 43.16) = less than 0.00001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis. Thus, we conclude that there is a relationship between Preference for computer type and highest degree.