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MATH 203 Sample Problems Unit 2
A politician claims that 70% of adults support a constitutional amendment to define marriage. But a poll of 1000 adults found that only 675 had this belief.
Does this poll give enough evidence to reject that 70% of all adults favor such an amendment?
(a) State the null hypothesis and an appropriate one-sided alternative.
(b) Show how to find the test statistic.
(c) If we use a 0.05 level of significance, then what endpoint gives the bound for rejecting the null hypothesis? Show it on the appropriate distribution curve. What about if = 0.025?
(d) Compute the P -value and explain the conclusion in detail based upon a 0.05 level of significance.
(e) Use the test statistic to explain whether or not we have evidence to reject H 0 with a
0.025 level of significance.
Cholesterol levels among women are normally distributed with = 15. A sampling of 400 women gave x = 171 with S = 14.6. We will test if the average level differs from
- Results from one-sided Z–Tests and T–Tests on the sample are given below:
(a) Is there evidence, with = 0.05, to conclude that the mean cholesterol level of women differs from 170? Explain which test to use, state the null hypothesis, a one- sided alternative, and use the appropriate P -value from above to explain your conclusion in detail.
(b) With = 0.05, what is the critical value endpoint of the rejection region for your one-sided test in Part (a)? Show it on a shaded graph and label the distribution used.
(c) Show how to find the test statistic used for the test in Part (a). Explain the conclusion in terms of the test statistic.
