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A random sample of n = 200 observations from a binomial
Chapter 7, Problem 115SE(choose chapter or problem)
A random sample of n = 200 observations from a binomial population yields \(\hat{p}=.29\).
a. \(\text { Test } H_{0}: p=.35 \text { against } H_{\mathrm{a}}: p<.35 \text {. Use } \alpha=.05 \text {. }\)
b. \(\text { Test } H_{0}: p=.35 \text { against } H_{a}: p \neq .35 \text {. Use } \alpha=.05\).
Questions & Answers
QUESTION:
A random sample of n = 200 observations from a binomial population yields \(\hat{p}=.29\).
a. \(\text { Test } H_{0}: p=.35 \text { against } H_{\mathrm{a}}: p<.35 \text {. Use } \alpha=.05 \text {. }\)
b. \(\text { Test } H_{0}: p=.35 \text { against } H_{a}: p \neq .35 \text {. Use } \alpha=.05\).
ANSWER:Answer
Step 1 of 2
(a)
A random sample of observations from a binomial population yields
Test
Using to denote the hypothesized value for the population proportion, the form for a hypothesis test about a population proportion are as follows.
Rejection rule for a lower tail test: The Critical Value Approach
……..(1)
Hence the test statistic for hypothesis tests about a population proportion,
………(2)
We have given
……….(3)
The rejection region requires
in the lower tail of the
From the table II, Appendix D, the value of
…….(4)
From equation (3) and (4) we can see that the observed value of the test statistic falls in the rejection region.
Since,
Hence is rejected and there is sufficient evidence to indicate that the population proportion is less than
at