Old Exam Questions Hypothesis Testing 1

1 Old Exam Questions -SolutionsHypothesis Testing (Chapter 7)1. First note that this is a claim about a population PROPORTION. Thus we will be using thesymbolp. Note that the claim can be written symbolically asp 14 The opposite of the claim isp 14 Since the claim does NOT contain equality, it becomes the alternative Hypothesis . Thehypothesis always has in it. Thus we haveH0:p 14H1:p 142. First note that the claim, null & alternative hypotheses areClaim: : : thepvalue ( ) is less than ( ), the conclusion about the null hypothesiswould be: Reject the null Hypothesis . Using Figure 7-7 on page 346, the final wordingabout the claim would be: "The sample data support the claim that the mean bodytemperature of adult humans is not degrees."3. Firstnotethatforthesampledatawehaven 23,x years, ands yearsWe do NOT know the population standard deviation and we are told to assume thepopulation distribution is normal.

2 Thus we will use thetdistribution to find critical , note that the claim, null & alternative hypotheses areClaim: 4H0: 4H1: 4 Thus we have a LEFT-tail test (we will need to make sure the critical value is negative!).We are told that and note that the degrees of freedom n-1 23 - 1 22. Thuslook in Table A-3 with (in ONE tail) anddf 22. We find that ourcritical Note that we had to include the negative sign since this was a LEFT-tail that the decision test will be that we will reject the null Hypothesis if our test statisticis less than ( ).4. Note we are Testing a claim about a population standard deviation. Thus critical values willcome from Table A-4 (chi-square distribution). We have a left tail test. Since ,the area to the RIGHT of the critical value must be 1 - .05 .95. Withdf 24the criticalvalue is The correct choice is (b).

3 5. Note that this is a claim about a population PROPORTION. We are given thatn 603 andp :p :p :p have a two-tail Values: (from Table A-2)Decision Test: Reject the null Hypothesis if or if Statistic:z p ppqn 603 Hypothesis Conclusion: Reject H0 Non-technical restatement: Thereissufficient evidence to warrant therejectionof theclaim that McDonald s is preferred by half of all To compute thepvalue for #5, we find the area under the standard normal curve to the leftof the test statistic and double it since we have a two-tail test (see Figure 7-6 on page 344).The test statistic was Using Table A-2, the area to the left of the test statistic Thus thepvalue is 2( ) This is a test of a population MEAN. We haven 35,x hours, ands hoursSincen 30 and the population standard deviation is unknown, we have : 7H0: 7H1: 7We have a left-tail test.

4 Thus the critical value is (From Table A-3 withdf 34 and in one tail). Hence the decision test is to reject the null Hypothesis if the teststatistic is less than The test statistics ist x sn the test statistic is not in the critical region, the conclusion is: Failure to reject thenull Hypothesis . Using Figure 7-7 on page 346 (and in your formula card), the wording ofthe final conclusion is: "There is NOT sufficient sample evidence to support the claim thatstatistics students spend less than 7 hours studying per week."8. We are Testing a claim about a population mean. We haven 7andx ands we are assuming that the population is normally distributed, we have : 9,000H0: 9,000H1: 9,000We have a right-tail Value: (t-test with 6 degrees of freedom and in one tail)Decision test: Reject the null Hypothesis Statistic:t x sn : Reject H0 Non-technical restatement: The sample dataSUPPORTthe claim that the mean annualconsumption amount is more than 9,000 We are Testing a claim about a population standard deviation.

5 We haven 22 ands claim is so we haveH0: : is a left-tail Value: (Table A-4 withdf 21 and so that area to right is 1 )Decision Test: Reject H0if TS Statistic: 2 n 1 s2 2 22 1 : Fail to reject H0 Non-technical restatement: There isNOTsufficient sample evidence to support the claimthat the standard deviation is less than millimeters.