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Magazine Problem 1
State the null and alternative hypotheses; calculate the appropriate test statistic; provide an \(\alpha=.05\) rejection region; and state your conclusions. A random sample of \(n=1000\) from a binomial population contained 279 successes. You wish to show that \(p<.3\)
Problem 1
Independent random samples were selected from two binomial populations, with sample sizes and the number of successes given. Use this information to calculate \(\hat{p}_{1}, \hat{p}_{2},\) and \(\hat{p}\). $$ n_{1}=1250, n_{2}=1100, x_{1}=565, x_{2}=621 $$
Problem 1
Define \(\alpha\) and \(\beta\) for a statistical test of hypothesis.
Problem 1
List the five parts of a statistical test.
Problem 2
Define the level of significance.
Problem 2
Independent random samples were selected from two binomial populations, with sample sizes and the number of successes given. Use this information to calculate \(\hat{p}_{1}, \hat{p}_{2},\) and \(\hat{p}\). $$ n_{1}=60, n_{2}=60, x_{1}=43, x_{2}=36 $$
Problem 2
For a fixed sample size \(n\), what is the effect on \(\beta\) when \(\alpha\) is decreased?
Problem 2
State the null and alternative hypotheses; calculate the appropriate test statistic; provide an \(\alpha=.05\) rejection region; and state your conclusions. A random sample of \(n=1400\) observations from a binomial population produced \(x=529\) successes. You wish to show that \(p\) differs from .4
Problem 3
State the null and alternative hypotheses; calculate the appropriate test statistic; provide an \(\alpha=.05\) rejection region; and state your conclusions. Seventy-two successes were observed in a random sample of \(n=120\) observations from a binomial population. You wish to show that \(p>.5\).
Problem 4
Calculate the p-value for the hypothesis tests given. $$ n=1000 \text { and } x=279 \text { . You wish to show that } p<.3 . $$
