MATH 10 De Anza College Hypothesis Testing and The Meaning of P Value Questions


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Lecture 12
A beginning statistics student claims that he nally understands the meaning of the p value.
When asked to summarize his newly acquired knowledge, he states: The p-value gives the probability that the null hypothesis is correct.” Explain why you agree or disagree. (8.1.7)
2. Suppose we are testing Ho : = 15 vs. Ha : > 15 and we have the following information:
= 9, x = 18, n = 36, and = 0.01. What is the conclusion? Answer: p-value = 0.0228
In your work for a national health organization, you are asked to monitor the amount of sodium
in a certain brand of cereal. You nd that a random sample of 52 cereal servings has a mean sodium
content of 232 milligrams. At = 0.04, can you conclude that the mean sodium content per serving
of cereal is greater than 230 milligrams? Assume = 10 milligrams. (F & L 7.2.42) Answer:
p-value = 0.0746
4. Environmental Science & Technology (October 1993) reported on a study of contaminated soil
in The Netherlands. Seventy-two 400-gram soil specimens were sampled, dried, and analyzed for
the contaminant cyanide. The cyanide concentration [in milligrams per kilogram (mg/kg) of soil]
of each soil specimen was determined using an infrared microscopic method. The sample resulted
in a mean cyanide level of x = 84 mg/kg. Test the hypothesis that the true mean cyanide level
in soil in The Netherlands exceeds 100 mg/kg. Use = 0.10. Assume = 80 mg/kg. Answer:
p-value = 0.955

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null hypothesis

Significance Level

the p value

the probability

Z values

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