Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic for
ID: 3152579 • Letter: E
Question
Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. Use the correct symbol (µ, p, )for the indicated parameter
1) An entomologist writes an article in a scientific journal which claims that fewer than 20 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.
A) H0: p = 0.002 H1: p < 0.002 B) H0: p > 0.002 H1: p K 0.002 C) H0: p < 0.002 H1: p L 0.002 D) H0: p = 0.002 H1: p > 0.002
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.
2) = 0.1 for a two-tailed test.
A) ±2.052 B) ±1.4805 C) ±1.645 D) ±2.33
Find the value of the test statistic z using z
3) A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n = 1813 subjects with 30% saying that they play a sport.
A) 17.03 B) -17.03 C) -34.77 D) 34.77
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.
4) In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief.
Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution.
5) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed below.
14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2
At the 0.01 significance level, test the claim that the mean weight is 14 ounces. 5)
Explanation / Answer
1) A) The alternative hypothesis is what the researcher claims.
2) C) For two-taled test, Z critical at alpha=0.10 is 1.645.
3) Z=(Ps-Pu)/sqrt [Pu(1-Pu)/N], where, Ps is the sample proportion, Pu is the population proportin, N is smaple size.
Z=(0.3-0.5)/sqrt [0.5(1-0.5)/1813]=-17.03 Option B)
4) H0:Pu=0.5, H1:Pu>0.5
Use preceding formula, with Ps=0.53, Pu=0.5
Z=(0.53-0.5)/sqrt [0.5(1-0.5)/108]=0.62
The p value is 0.267. The p value is not less than alpha=0.01. Therefore, fail to reject null hypothesis. There i snot sufficient sample evidenceto conclude that more than half of all those using the drug experience relief.
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