A researcher is wondering whether the drinking habits of adults in a certain reg

Question

A researcher is wondering whether the drinking habits of adults in a certain region of the country are in a higher proportion than the general population of adults. Suppose a recent study stated that the proportion of adults in the population who reported drinking once a week or less in the last month was p = 0.26. The researcher decides to collect data from adults working in “blue collar” jobs to see whether their drinking habits are in a higher proportion than the general public. The researcher collected data from a random sample of 90 adults with “blue collar” jobs of which 30 stated that they drank once a week in the last month. Perform the hypothesis test with = .05.

Name of Test: __________________________________________

A. Hypothesize:

H0:

Ha:

B. Prepare: = 0.05

     Check the Central Limit Theory Conditions: Show the work and numbers on successes and failures.

C. Compute to Compare: Draw the sampling distribution marking the critical region(s) with the z*. Find the test statistic and the p-value in your calculator. Be sure to give the letter for the test statistic.

D. Interpret. Give your conclusion and statement.

Explanation / Answer

This is a test of proportion

P = 0.26

p = 30/90 = 0.33

A) H0: P = 0.26

H1: P > 0.26

Standard deviation = sqrt(P * (1 - P)/n)

= sqrt (0.26 * 0.74/90)

= 0.046

At alpha = 0.05, the critical value is Z* = 1.96

The test statistic Z = (p - P)/SD

= (0.33 - 0.26)/0.046

= 1.52

P-value = P(Z > 1.52)

= 1 - P(Z < 1.52)

= 1 - 0.9357

= 0.0643

As the p-value is greater than the alpha value 0.05 so the null hypothesis is not rejected.

SO the claim that the drinking habits of adults in a certain region of country are in a higher proportion than the general population of adults is rejected.

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