Question

According to the 2017-2018 U.S. Pet Ownership & Demographics Sourcebook, 38.4% of US households own a dog. Ms Ferguson believes the percent of households who own a dog has changed since 2018, so she polls 90 students and finds that 39 students own a dog. Test Ms. Ferguson’s claim at the α = 0.05 significance level. Regardless of which method you use, sketch a graph showing the critical region and where the test statistic falls - inside or outside the critical region.

Answer 1

H0: p = 0.384

Ha: p 0.384

Sample proportion = 39 / 90 = 0.4333

Test statistics

z = ( - p) / sqrt [ p ( 1 - p) / n ]

= ( 0.4333 - 0.384) / sqrt [ 0.384 ( 1 - 0.384) / 90 ]

= 0.96

Critical value at 0.05 level = -1.96 , 1.96 (From Z table)

Rejection region = Reject H0 if z < -1.96 OR z > 1.96

Shaded region is critical value rejection region.

Since test statistics falls in non-rejection region (test statistics falls outside critical region ) ,

fail to reject H0