Question

A study conducted in June 2015 examines ownership of tablet computers by US adults. A random sample of people were surveyed, and we are told that of the men own a tablet and of the women own a tablet. We want to test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women. Let group be US men and let group be US women.

Answer 1

Answer:

a) The null hypothesis

H₀: P₁ = P₂

The alternative hypothesis

Hₐ: P₁ ≠ P₂

The proportion of the women population that own a tablet is P₁

And the proportion of the men population that own a tablet is P₂

b) The sample statistics are p₁ and p₂ for women and men sample proportions that own a tablet respectively.

p₁ = 0.4663

p₂ = 0.4330

The difference in sample proportion of tablet owners = p₁ - p₂ = 0.4663 - 0.4330 = 0.0333 (not 0)

Hence, the alternative hypothesis is true.

Step-by-step explanation:

The null hypothesis is the one that predicts no difference in tablet ownership.

The alternative hypothesis is the one that proves the initial theory of the survey that there is a difference in the proportion of men and women populations that own a tablet.

If the proportion of the women population that own a tablet is P₁

And the proportion of the men population that own a tablet is P₂

Then, the sample proportion of women that own a tablet = p₁

Sample proportion of men that own a tablet = p₂

The null hypothesis, H₀, stated mathematically, is

H₀: P₁ = P₂

The alternative hypothesis, Hₐ, stated mathematically, is

Hₐ: P₁ ≠ P₂

b) Like I stated in (a) the sample statistics are p₁ and p₂ for women and men sample proportions that own a tablet respectively.

From the data given,

p₁ = (235/504) = 0.4663

p₂ = (197/455) = 0.4330

In the sampled group, the women group have a higher proportion of tablet owners.

The difference in sample proportion of tablet owners = p₁ - p₂ = 0.4663 - 0.4330 = 0.0333

Hence, the alternative hypothesis is true.

Hope this Helps!!!