Question

According to a study conducted by an​ organization, the proportion of americans who were afraid to fly in 2006 was 0. 10. A random sample of americans results in indicating that they are afraid to fly. Explain why this is not necessarily evidence that the proportion of americans who are afraid to fly has.

Answer 1

According to the the concept of hypothesis testing, there is no evidence that the proportion of Americans who are afraid to fly has decreased.

Hypothesis testing:

Basically, in math hypothesis, it test the population on the basis of the sample data taken from the population using a simple random sampling.

Given,

According to a study conducted by an​ organization, the proportion of Americans who were afraid to fly in 2006 was 0. 10. A random sample of 1300  Americans results in 117 indicating that they are afraid to fly.

Now, we need to explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has.

While we looking into the given question,

Sample size, n = 1300

Number of Americans who were afraid to fly, x = 117

Now, we have to computing the sample proportion of Americans who afraid to fly,

Therefore, p = 117 / 1300 = 0.09

Then the Formulation of Hypotheses is written as,

Here the Null Hypothesis: H0: p≥0.10

And the alternative Hypothesis: Ha: p<0.10

Then the Left-tailed test of Test statistic is written as,

Here Let us assume that the level of significance, α = 0.05.

Then the Critical value, z≈−1.645

And the Decision rule is written as

If the value of  |z|<|z0.05|≈1.645: Do not reject the null hypothesis.

Otherwise If value of  |z|≥|z0.05|≈1.645: Reject the null hypothesis.

To know more about Hypothesis testing here.

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