4. A researcher claims that the incidence of a certain type of cancer is < 5%. To test this claim, a
random sample of 4000 people are checked and 170 are found to have the cancer.
The following is the set up for the hypothesis:
Ho = 0.05
Ha = < 0.05
In the example the p-value was determined to be 0.015.
Come to a conclusion and interpret the results of this hypothesis test for a proportion (use a significance level of 5%)
Answer: The decision is to reject the null hypothesis. The conclusion is that there is enough evidence to support the
claim.
5. A researcher is investigating a government claim that the unemployment rate is < 5%. TO test this
claim, a random sample of 1500 people is taken and it is determined that 61 people were
unemployed.
Ho: p = 0.05 Ha: p < 0.05
Find the p-value for this hypothesis test for a proportion & round to 3 decimal places.
Hypothesis Test for p
population proportion
Level of Significance 0.05
Proportion under H0 0.0500
n 1500
Number of
Successes 61
Sample Proportion 0.040667
StDev 0.217945
SE 0.005627
-
Test Statistic (z) 1.658577
One-Sided p-value 0.048457
Two-Sided p-value 0.096914
Answer: 0.048
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