Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 8 - Hypothesis Testing - 8-3 Testing a Claim About a Proportion - Basic Skills and Concepts: 5

Answer

a)Left-tailed. b)z=-1.942721717. c)P=0.0260248259. d)p=0.1, reject null hypothesis e)There is sufficient evidence to support that the proportion of experienced headaches is less than 0.1.

Work Step by Step

a) The alternative hypothesis is: p<0.1. If the alternative hypothesis contains $\ne$ then the test is two-tailed. If the alternative hypothesis contains < then the test is left-tailed. If the alternative hypothesis contains > then the test is right-tailed. Hence it is left-tailed. b) The value of the test statistic is: z=-1.942721717. c)The value of P is: P=0.0260248259. d)By using the alternative hypothesis the null hypothesis says: p=0.1. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P=0.0260248259 is less than $\alpha=0.05$, hence we reject the null hypothesis. e)By d) we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the proportion of experienced headaches is less than 0.1.
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