Question

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 at the 5% level to determine if the rate is still 14% or if it has decreased.

A. What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)
B. What is the p-value? (Round your answer to four decimal places.)
C. Construct a 95% confidence interval for the true mean or proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to four decimal places.)

Answer 1

Answer:

a)

Given,

sample proportion p^ = x/n = 9/70 = 0.1286

Ho : p = 0.14

Ha : p < 0.14

test statistic z = (p^ - p)/sqrt(pq/n)

substitute values

= (0.1286 - 0.14)/sqrt(0.14(1-0.14)/70)

= - 0.28

b)

P value = 0.3897388 [since from z table]

= 0.3897

Here we observe that, p value > alpha, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.

c)

Here at 95% CI, z value is 1.96

95% CI = p^ +/- z*sqrt(p^q^/n)

substitute values

= 0.1286 +/- 1.96*sqrt(0.1286(1-0.1286)/70)

= 0.1286 +/- 0.0784

= (0.0502 , 0.2070)