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Chapter 9: Q. 100 (page 553)

According to an article in Bloomberg Businessweek, New York City's most recent adult smoking rate is 14%. Suppose that a survey is conducted to determine this year’s rate. Nine out of 70 randomly chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still 14% or if it has decreased.

Short Answer

Expert verified

The hypothesis test has resulted in ap-value greater than the alpha value and the null hypothesis is not rejected and the rate is still at 14%.

Step by step solution

01

Given information

The adult smoking rate=14%

02

Explanation

State the hypothesis:

The null hypothesis states that 14%of adults do smoke and the alternate hypothesis states that not more than 14%of adults do smoke.

H0:p=0.14H0:p<0.14

The normal distribution is:

N0.14,0.140.8670

The Z test statistic is:

z=p∧-pp1-pnP∧=xn=970=0.129

Substitute the p∧value in the Z statistic formula

z=p∧pp1-pn=-0.011430.0415=0.2756

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