Question

A communications company has developed three new designs for a cell phone. To evaluate consumer response, a sample of n = 120 college students is selected and each student is given all three phones to use for one week. At the end of the week, the students must identify which of the three designs they prefer. The distribution of preference is as follows: Design 1=54, Design 2=38, Design 3=28. Do the results indicate any significant preferences among the three designs?

Answer 1

Answer:

The answer is "Its results are not consistent with its three designs Yes. Its results show significant differences between both the three designs."

Step-by-step explanation:

Following are the distribution of preference:  

$Design 1 =54 \\\\ Design 2=38 \\\\\ Design 3=28$

$Design \ \ \ \ \ \ \ \ \ \ O_i \\ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 54 \\2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 38\\3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 28 \\Total \ \ \ \ \ \ \ \ \ \ 120$

An expected frequency($E_i$) has 40 Null hypotheses to take n=120.to each design:  

The effects of the three designs are standardized  

Inaccurate.  

Hypothesis Alternative:  

The effects of the three prototypes are not uniform

Degrees Of freedom $=(n-1)=(3-1)=2$

$H_o, x^2 \ test\ statistic \ \sum_i {\frac{(O_i -E_i)^2}{E_i}}$

$= \frac{(54 -40)^2}{40}+\frac{(38-40)^2}{40} + \frac{(28-40)^2}{40}\\\\=49+0.1+3.6\\\\=8.6$

Chi-squared distribution critical value at $\alpha = 0.05 (x^2 _{0.052})=5.99$  

Since $x^2, a$ value $> x^2 -$table of $\alpha =0.05 =5.99$is determined.  

So$H_o$ is rejected.