Question

Complete a 6-step hypothesis test using the following scenario:

The body mass index (BMI) of an individual is a measure used to judge whether an individual is overweight or not. A BMI between 20 and 25 indicates normal weight. In a survey of 750 men and 750 women, the Gallup organization found that 203 men and 270 women were normal weight. Is this enough evidence to determine if there is a greater number of women at a normal weight than men overall? Use a 0.05 significance level.

Answer 1

H₀: P1 = P2

H₁: P1 < P2

= 203/750 = 0.271

= 270/750 = 0.36

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                                     = (0.271 * 750 + 0.36 * 750)/(750 + 750)

                                                     = 0.3155

SE = sqrt(P(1 - P)(1/n1 + 1/n2))

     = sqrt(0.3155 * (1 - 0.3155) * (1/750 + 1/750))

     = 0.024

The test statistic z = ( - )/SE

                             = (0.271 - 0.36)/0.024

                             = -3.71

At alpha = 0.05, the critical value is z_0.05 = -1.645

Since the test statistic value is less than the critical value(-3.71 < -1.645), so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to conclude that there is a greater number of women at a normal weight than men overall.