Question

Nation teen driving statistics claims that 65% of the Americans think that teenagers are the most dangerous drivers. Gallup Poll think that this proportion is different. Gallup Poll surveyed 900 randomly sampled Americans and found that 63% would rate teenagers as the most dangerous drivers.

1. Conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who think that teenagers are the most dangerous is different from 65%. Use α=0.05. Use correct symbols and formulas. Interpret the results.

• What is your population parameter?
• State the hypotheses.
• Check appropriate conditions for a hypothesis test and name the model. Sketch 68-95-99.7 rule in the graph given

Calculate the test statistic including the P-value.

State your conclusion in the context of the given study.

Answer 1

The national teen driving statistics is the population proportion,

P0 = 0.65

The gallup poll is the sample proportion,

p̂ = 0.63

The hypothesis is,

The population and sample mean are same

The population and sample mean are not the vsame

We know that,

Where, n = 900

Therefore,

Z = (0.63 - 0.75)/0.0259

Z = - 1.2579

The p value is,

P = 0.1042

Since the p value is greater than level of significance (0.1042 > 0.05). We fail to reject the null hypothesis. We fail to reject that the population proportion and sample proportion are same.