Question
Perform a hypothesis test. Students should decide from the context which kind of test (mean, proportion, or variance/standard deviation) and which distribution to use.
11. Perforna a hypothesis test. Students should decide from the contest which kind of test (nean, proportion, or variance/standard deviation) and which distribetion to ase. In 2003, random o a journalist claimed that over 43% of Americans own a costul" peens. lax cellular phone. Test the journalist's claim at -0.10, Cle-lynicae -the null and alternative hypotheses the critical value(s) or P-value -the standardized test statistic -your conclusion (don't just say "Reject Ho" or "Doe't reject H"-tell whether the journalist's claim is justified) o An insurance company states that at least 79% of its claims are settled within month. A consumer group selected a random sample of 172 claims and found that 115 of them were settled within a month. Test the insurance company's claim at a 0.05. Clearly indicate (a) the null and alternative hypotheses, (b) the critical valuefs) or P-value. (e) the standardized test stactistic, and (d) your conclusion in the context of the situstion. o A humane society claims that 34% ofUS, bouseholds own a cat. In a random sample of 220 U.S. households, 65 own a cat. Test the socicty's claim at -0.10 Clearly indicate (a) the null and alternsative hypotbeses, (b) the critical valueis) or P. value, (c) the standardized test statistic, and (d) your conclusion in the context of the situation, A student group believes that the mean cost of used textbooks is more than $136. To test this claim, the group randomly samples 47 used textbooks and finds a mean cost o of $140.44. A prior study found that the standard deviation of all textbook costs is SI 9.47. Using -001, test the student group's belief, Clearly indicate (a) the null and alternative hypotheses, (b) the critical valuels) or P-value, (c) the standardized test statistic, and (d) your conclusion in the context of the situation. An automotive battery manufacturer guarantees that the mean reserve capacity of a certain battery is greater than 1.5 hours. To test this claim, you randomly select a sample of 51 batteries and find the mean reserve capacity to be 1.55 hours with a o standard deviation of 0.32 hour. At -0.10, test the manufacturer's claim. Clearly indicate -the null and alternative hypotheses -the critical valuc(s) or P-value -the standard score your conclusion (don't just say "Reject Ho" or "Don't reject Ho" tell whether the manufacturer's claim is justified)
Explanation / Answer
11)
Ho: p = 0.43
Ha: p > 0.43
X = 456 , n = 1036
critical value = 1.282
TS = (p^ - p)/sqrt(pq/n)
= (456/1036 - 0.43)/sqrt(0.43 *0.57/ 1036)
= 0.660182
p-value = P(Z> 0.660182) = 0.255
since TS < critical value
we fail to reject the null hypothesis
