Question

Your marketing team has conducted two focus group sessions to evaluate a new product design. The first focus group consisted of teenagers and resulted in four out of five liking the new product. The second group was made up of parents of young children. Only one out of five people in this group said they liked the same new product as the teens. With 90% confidence (Z = 1.64), can you say that there is a difference between the views of these two populations? Please show your calculations, use 2 decimal places in your calculation answer, and justify your answer regarding differences.

Answer 1

Since the calculated Z falls in the critical region therefore the null hypothesis is rejected and concluded that there is a difference between the views of these two populations.

Explanation:

1) Formulate the hypotheses:

H0 : p1=p2

Ha: p1 ≠ p2

2) The significance level is chosen at ∝= 0.1

3) The critical region is Z∝/2 ≥ ± 1.645

4) The test statistic under H0 is

Z = p1^- p2^/ √p^q^( 1/n1 + 1/n2)

p1^= proportion of of teenagers liking the new product.

p2^ = proportion of of parents of young children liking the new product.

p1^= 4/5

p2^= 1/5

p^= 5(0.8) + 5(0.2)/5+5= 4+1/10= 0.5

q^= 0.5

Thus

Z= p1^- p2^/ √p^q^( 1/n1 + 1/n2)

z= 0.8-0.2/√0.5*0.5( 1/5 + 1/5)

z= 0.6/ 0.316227

z= 1.897

5) Conclusion:

Since the calculated Z falls in the critical region therefore the null hypothesis is rejected and concluded that there is a difference between the views of these two populations.