A random group of desktop computer sales was selected from an electronic discount chain to analyze the size of monitor purchased with the computer. Is there evidence to reject the hypothesis that the number of monitors is equally distributed between the five types, at $= .05$ ? $\begin{array} { c c c c c c } \text { Monitor type } & 15 " \text { CRT } & 15 " \text { flat panel } & 17 \text { " CRT } & 17 ^ { \prime \prime } \text { flat panel } & 19 " \text { CRT } \ \text { Number of sales } & 16 & 24 & 14 & 9 & 4 \end{array}$ A)There is evidence to reject the claim that the monitors are equally distributed between the five classes because the test value $16.955 11.070$ B) There is not evidence to reject the claim that the monitors are equally distributed between the five - classes because the test value $9.488 9.488$ D)There is not evidence to reject the claim that the monitors are equally distributed between the five . classes because the test value $11.070

Question

A random group of desktop computer sales was selected from an electronic discount chain to analyze the size of monitor purchased with the computer. Is there evidence to reject the hypothesis that the number of monitors is equally distributed between the five types, at $= .05$ ? $\begin{array} { c c c c c c } \text { Monitor type } & 15 " \text { CRT } & 15 " \text { flat panel } & 17 \text { " CRT } & 17 ^ { \prime \prime } \text { flat panel } & 19 " \text { CRT } \ \text { Number of sales } & 16 & 24 & 14 & 9 & 4 \end{array}$ A)There is evidence to reject the claim that the monitors are equally distributed between the five classes because the test value $16.955 > 11.070$ B) There is not evidence to reject the claim that the monitors are equally distributed between the five - classes because the test value $9.488 < 10.361$ C)There is evidence to reject the claim that the monitors are equally distributed between the five classes . because the test value $16.955 > 9.488$ D)There is not evidence to reject the claim that the monitors are equally distributed between the five . classes because the test value $11.070 < 10.361$

Quizplus · Accepted Answer

We can use a chi-square goodness-of-fit test to determine whether the number of monitors sold is equally distributed among the five types. The null hypothesis is that the monitors are equally distributed among the five types, while the alternative hypothesis is that they are not. The chi-square test statistic is calculated as:

$$\chi^{2}=\sum_{i=1}^{k} \frac{(O_{i}-E_{i})^{2}}{E_{i}}$$

where Oi is the observed frequency of type i and Ei is the expected frequency of type i, assuming equal distribution. The degrees of freedom are k-1, where k is the number of types.

Using the given data, we can calculate the expected frequencies as follows:

Expected frequency = Total number of sales / 5

Expected frequencies:

15" CRT: (16+24+14+9+4)/5 = 13.4
15" flat panel: (16+24+14+9+4)/5 = 13.4
17" CRT: (16+24+14+9+4)/5 = 13.4
17" flat panel: (16+24+14+9+4)/5 = 13.4
19" CRT: (16+24+14+9+4)/5 = 13.4

We can then calculate the chi-square test statistic:

$$\chi^{2}=\frac{(16-13.4)^{2}}{13.4}+\frac{(24-13.4)^{2}}{13.4}+\frac{(14-13.4)^{2}}{13.4}+\frac{(9-13.4)^{2}}{13.4}+\frac{(4-13.4)^{2}}{13.4}=16.955$$

The degrees of freedom are 5-1=4. Using a chi-square distribution table with 4 degrees of freedom and a significance level of 0.05, we find the critical value to be 9.488. Since the calculated test statistic of 16.955 is greater than the critical value of 9.488, we can reject the null hypothesis and conclude that there is evidence to suggest that the monitors are not equally distributed among the five types. Therefore, our answer is C.

A Random Group of Desktop Computer Sales Was Selected from an Electronic