Question

In 1950​, an organization surveyed 1100 adults and​ asked, "Are you a total abstainer​ from, or do you on occasion​ consume, alcoholic​ beverages?" Of the 1100 adults​ surveyed, 363 indicated that they were total abstainers. In a recent​ survey, the same question was asked of 1100 adults and 319 indicated that they were total abstainers. Has the proportion of adults who totally abstain from alcohol​ changed? Use the α = 0.01 level of significance. Normality criteria have been satisfied.

Write the Null and Alternative Hypothesis:

Give the Test statistic and P value:

State the conclusion in context:

Answer 1

p₁ : Population proportion of adults who totally abstain from alcohol​ when surveyed in 1950

p₂ : Population proportion of adults who totally abstain from alcohol​ in recent survey

Null hypothesis H_o: p₁ = p₂

Alternate hypothesis :H_a p₁ p₂

Since the null hypothesis states that p1=p2, we use a pooled sample proportion () to compute the standard error of the sampling distribution.

Given
n1 : Sample Size of survey in 1950	1100
n2 : Sample Size of recent survey	1100
x1: Number of adults indicated that they were total abstainers from the survey in 1950	363
x2: Number of adults indicated that they were total abstainers from the recent survey	319
: Sample Propotion of adults indicated that they were total abstainers from the survey in 1950	0.33
: Sample Propotion of adults indicated that they were total abstainers from the recent survey	0.29
Level of Significance	0.01

Two Tailed Test: P-value :

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0425 > 0.01:Level of significance); Fail to Reject Null Hypothesis

At , 0.01 level of significance , the evidence is not sufficent to reject that the proportion of adults who totally abstain from alcohol​ has not changed