ANS:2= 4.25; p-value (0.3732) is larger than 0.1; do not reject Ho; no difference (critical 2= 9.488)PTS:1TOP:Hypothesis Testing26.A lottery is conducted that involves the random selection of numbers from 0 to 4. To make sure that the lottery is fair, a sample of 250 was taken. The following results were obtained.ValueFrequency040145255360450a.State the null and alternative hypotheses to be tested.b.Compute the test statistic.c.The null hypothesis is to be tested at the 5% level of significance. Determine the critical value from the table.d.What do you conclude about the fairness of this lottery?ANS:a.H0: p0= p1= p2= p3= p4= 0.2Ha: The population proportions are not p0= p1= p2= p3= p4= 0.2b.5c.9.488d.Do not reject the null hypothesis; it is fair. (p-value = 0.2872)PTS:1TOP:Hypothesis Testing27.The makers of Compute-All know that in the past, 40% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 15% of their sales were from people who are over 50 years old. A sample of 300 customers was taken to see if the market shares had changed. In the sample, 100 of the people were under 30 years old, 150 people were between 30 and 50 years old, and 50 people were over 50 years old.a.State the null and alternative hypotheses to be tested.b.Compute the test statistic.c.The null hypothesis is to be tested at the 1% level of significance. Determine the critical value
from the table.d.What do you conclude?ANS:a.H0: p1= 0.4, p2= 0.45, and p3= 0.15Ha: The population proportions are not p1= 0.4, p2= 0.45, and p3= 0.15b.5.56c.9.210d.Do not reject the null hypothesis (p-value = 0.062); market share hasn't changed.PTS:1TOP:Hypothesis Testing28.The following table shows the results of a recent study regarding the gender of individuals and their selected field of study.Field of StudyMaleFemaleTOTALMedicine8040120Business602080Engineering16040200TOTAL300100400We want to determine if the selected field of study is independent of gender.a.Compute the test statistic.b.Using the p-value approach at 90% confidence, test to see if the field of study is independent of gender.c.Using the critical method approach at 90% confidence, test for the independence of major and gender.ANS:a.2= 7.11b.p-value (0.0286) is between .025 and .05; reject Ho; field of study is not independent of genderc.critical 2= 4.605; reject HoPTS:1TOP:Hypothesis Testing
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- Spring '10
- Calculus, Null hypothesis, Hypothesis testing, Statistical hypothesis testing