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In 2005, 39.4% of females had ordered merchandise or services by phone in
the last 12 months. A market research analyst feels that the percentage of females
ordering merchandise or services by phone has declined from the 2005 level
because of Internet purchases. He obtains a random sample of 500 females and
determines that 191 of them have ordered merchandise or services by phone in the
last 12 months.
a) Test the research analyst’s claim at the α=0.10 level of significance.
Null Hypothesis H0: Population Proportion = 0.394 Alternate Hypothesis H1: Population Proportion < 0.394 Significance Level α = 10% The name of the TI-83/84 calculator function you will be using: 1-PropZTest Are the conditions met in order to use this statistical method? Show how you
YES. We have a random sample from a huge population, and our sample size is large enough
to pass this test (for "p" you can use either the hypothesized value or the sample proportion):
np(1-p) = (500)(0.394)(1-0.394) = 119.382 > 10; So our Sampling Distribution for the sample
proportion should be approximately normal. The values that you entered into your TI-83/84 calculator: p0 : 0.394
x: 191 n: 500 prop: < P0 ← (show which choice you highlighted) From your calculator’s output give the following:
Test Statistic z = -0.55 Interpret what this value is telling you: Our Test Statistic is 0.55 of a Standard Error below the hypothesized population
proportion of 0.394; this is not very far away.
P-Value = 29.15% Interpret what this value is telling you: There is a 29.15% probability of getting a Test Statistic this far below (or farther below)
the hypothesized population proportion of 0.394 IF the Null Hypothesis is true.
Page 4 of 9 Which one is your conclusion (Click in the box next to your choice):
Failed to Reject H0
Reject H0 and Accept H1
Show the reason for your conclusion (Click in the box next to your choice): P-value > Significance Level
29.15% > 1...
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- Winter '08