Question

A researcher is interested in consumer preferences among three brands of yogurt. A sample of 90 people is obtained,

Answer 1

Answer:

Step-by-step explanation:

From the given information:

The null hypothesis: all three brands are equally likely to their expected value

The alternative hypothesis: preferences exist among the three brands i.e. at least one is different from the expected value.

The expected frequency = $f_e$  

The observed frequency = $f_o$

$f_e$                    $f_o$                      $(f_o- f_e)^2$                       $\dfrac{(f_o - f_e)^2}{f_e}$

37                   30                       49.00                        1.633

21                    30                        81.00                        2.700

32                   30                         4.00                         0.133

                                                                $X^2 = \sum\dfrac{(f_o-f_e)^2}{f_e} = 4.47$

Degree of freedom = $(n-1)$

= 3 -1

= 2

At ∝ = 0.05 and df = 2

The critical value $X^2_{0.05, 2}= 5.99$

Decision rule:

Since the calculated chi-square is less than the critical value, we do not reject the null hypothesis.

Thus, the null is retained with a calculated chi-square value of 4.47 and a critical chi-square value of 5.99.