Question

a research center claims that 16% of us adults say that curling is the winter olympic sport they would like to try the most. in a random sample of 300 us adults, 20% say that curling is the winter olympic sport they would like to try the most. at level of significance of 0.05, is there enough evidence to reject the researcher's claim?

Answer 1

At a 0.05 significance level, we don't have adequate proof to dismiss the claim that 16% of US adults prefer curling as their top winter Olympic sport. Yet, this conclusion relies on a sample and might not represent the actual population proportion.

How to solve

Null Hypothesis (H ₀): The proportion of US adults who say curling is their favorite winter Olympic sport is 16%.

Alternative Hypothesis (H₁): The proportion of US adults who say curling is their favorite winter Olympic sport is different from 16%.

Level of Significance (α): 0.05

Sample Size (n): 300

Sample Proportion (p): 20%

Test Statistic:

We will use the z-statistic to test this hypothesis. The formula for the z-statistic is:

z =
`(p - p) / \sqrt(p * (1 - p) / n)`

where:

p is the sample proportion (20%)

p is the population proportion (16%)

n is the sample size (300)

Calculating the z-statistic:

z =
`(0.20 - 0.16) / \sqrt(0.16 * (1 - 0.16) / 300)`

z ≈ 1.73

Decision Rule:

We will reject the null hypothesis if the z-statistic falls outside the critical region. At a level of significance of 0.05 and a two-tailed test, the critical region consists of values less than -1.96 or greater than 1.96.

Decision:

Our calculated z-statistic (1.73) is within the critical region (between -1.96 and 1.96). Therefore, we fail to reject the null hypothesis.

At a 0.05 significance level, we don't have adequate proof to dismiss the claim that 16% of US adults prefer curling as their top winter Olympic sport. Yet, this conclusion relies on a sample and might not represent the actual population proportion.