Lecture Note: Introductory Statistics, 9.1-9.5

Math& 146Fall 2023Name: Mia HamiltonWorksheet 08, 50 pointsContent: Introductory Statistics, 9.1-9.5Due: Tuesday, November 21version of your worksheet to Canvas by 11:59pm on November 21.You may either turn this in at the end of class Tuesday, November 21, or upload a pdfEach problem is worth 10 points. Your final score will be scaled out of 50 points.1) Do the following:a) and Translate the following claims to its symbolic form using appropriate symbols and notationb) which hypothesis represents theIndicate write claim.the symbolic form of the hull hypothesis and the alternative hypothesis.c) Indicate if the test is left-, right-, or two-tailed.quarters. Claim: The mean number of quarters required to complete a two-year degree is more than 6.3a Claim : M>63quartersb Ho : M 1663Ha: M7 6.3 CClaim)C night tail testif the mean is greaterbecause we actestingthan a certain value1 Problems 2-3: Do the following:a) State the null hypothesis, the alternative hypothesisb) Indicate if the test is left-, right-, or two-tailedc) State the decisiond) Write the conclusion in non-technical terms.2) Claim: > 87.2; a = 0.05; p-value = 0.04999) Ho: Mc 87.2HA: M>87.2b) Right tailed test because there testing if the meanis greater than a certain valueo) Reject the null hypothesisd)3) Claim: p 0 207; a = 0.01; p-value = 0.0241Ho: P20.207HA: p20.207Loft-tailed because certain value isnow less than the meanFail to reject Ho Cp vaule sa?No)2 Assume that a simple random sample has been selected from a normally distributedpopulation.Do the followingState the symbolic form of the claim and each hypothesis.Determine the test statistic (rounded to two-decimal places).Determine the p-value (rounded to 4 decimal places).State the decision (reject or fail to reject H0).State the conclusion in non-technical terms.Answer the follow-up question.4) A pharmaceutical company states that their new drug is effective in reducing asthma attacksfor more than 90% of those using it. This experimental drug was tested in a randomizedcontrolled trial. Among 292 subjects using the drug, 281 had a reduction in the frequency ofasthma attacks.Use a 0.01 significance level to test the claim that more than 90% of those using theexperimental drug had a reduction in their frequency of asthma attacks.Originalclaim: P70.90TestHo: pc 0.90Statistic:4.76H1: p>0.90less thanP-Value: 0.001Decision:Since the p-vaule less than the significance level, we reject Ho.Conclusion:The more data than providies strong evidence to support the claim thatin their freq 90% of of asthma those attacks. using the dong had a reductionFollow upThe should Statistical also test provides strong evidence however, theyconsider other factors ,such as sideeffective ness,effects other than that these proves the drug 3 Assume that a simple random sample has been selected from a normally distributedpopulation.Do the followingState the symbolic form of the claim and each hypothosis.Determine the test statistic (rounded to two-decimal places).Determine the p-value (rounded to 4 decimal places).State the decision (reject or fall to reject II,State the conclusion in non-technical terms.Answer the follow-up question.5) Students In a particular statistics class were asked to estimate the number of hours of sleepthey had the previous night. The data appear to be from a population that is normallydistributed, and those data are listed below.7.57.598,56.598.187.26.287.511.4997697.588.36.57Assuming those data represent typical sleep patterns, uso a 0.01 significance level to test theclaim that, on average, students get less than 8 hours of sleep on a typical night.Distribution: NormalOriginalclaim: M<8haurs2Ho: mz 8hrsStatistic: Test -1.64H1: MS 8hrsP-Value: 6.0505Decision:P-vanle is greater than SL, wefail to reject the Ho.Conclusion:There is notenogh evidence to support the claim thatstudents get less than Shos of sleep on avgFolloweepThe orginal claim that students get less than 4 Shrsof stepps on avg. isht supported by data