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MAT122-2005SpringUC

# MAT122-2005SpringUC - MATH 122 UC FINAL EXAM 9TH MAY 2005...

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Unformatted text preview: MATH 122 UC FINAL EXAM 9TH MAY 2005 Name ..................................................... .. SUID ............................ . . There are 7 questions in this booklet. Check that your exam booklet is complete. Answer the questions in the spaces provided in this exam booklet. Partial credit requires some correct and appropriate work. A sketch will be helpful in ﬁnding the critical region and the critical values Question Points - 3 l4 4 F 20 5 l4 1. [14 pts] A cereal company claims that the sodium content in one serving of its cereal is no more than 230 mg. John, an employee working for a national health service is asked to test this claim. He ﬁnds that a random sample of 52 servings has a mean sodium content of 232 mg and a standard deviation of] 0 mg. Using a signiﬁcance level of a = 0.05, does John have enough evidence to reject the company’s claim? 2. [14 pts] A certain economist conducted a survey of 740 randomly selected rural households and found that 290 of them have Internet access. She further conducted a survey of 800 urban households and found that 350 of them have Internet access. Use the data from these surveys and a significance level of 0.05 to test the claim that the proportion of those with Internet access is the same in both cases. 3. [14 pts] 100 volunteers at a certain research institute caught a cold after having been exposed to various cold viruses. 60 of the volunteers were randomly selected to be in the treatment group where they vitamin C tablets, which Were to be taken four times a day. The control group, consisting of the other 40 volunteers, was given placebo. The following results are measurements of the length of time the cold lasted. Vitamin C Placebo Treatment rou Control rou (a) [7 pts] Use a 0.05 significance level to test the claim that the mean time for patients treated with vitamin C is less than the mean time for the patients treated with placebo. (Do not assume that 0'1 2 02). (b) [7 pts] Construct a 90% conﬁdence interval estimate of the difference between the two population means. Write a statement that interprets the resulting confidence interval. 4. [20 pts] T he following table shows the annual salaries (in million) of various TV hosts and the number of viewers (in millions). In a study involving children 's fear related to being hospitalized, the age and the score that 7 children made on the Child Medical Fear Scale (CMF S) are given in the table below. 7 8 6 8 9 7 3 CMFS (y) 8 9 7 10 11 9 2 Given that: (a) [6 pts] Find the value of the linear correlation coeﬁ‘icient, r. (b) [6 pts] Using a signiﬁcance level of a = 0.05 determine whether there is a signiﬁcant linear correlation between age and CMFS. (c) [6 pts] Find the equation of the regression line. ((1) [2 pts] Find the best-predicted value of CMFS for a child aged 11 years. 5. [14 pts] The ofﬁce of international students (013) in a certain university claims that the international student population is approximately 45% Asians, 20% Europeans, 25% Africans and 10% others. In order to test this claim the MAT 122 class sampled 500 international students in this university and found 229 Asians, 105 Europeans, 122 Africans and 44 others. Conduct a hypothesis test using a significance level of a =0.05 to test the “goodness of ﬁt " of the distribution in the sample to the distribution in the international student population at large. Did the MAT 122 class ﬁnd evidence to support the claim that the distribution of the International students is as claimed by 013? 6. [14 pts] It may be of interest to see if the use of cellular phones while driving has any relation with automobile accidents. A study of randomly selected car accidents and drivers who use cellular phones are given below. Cellular Phone use and Accidents Had Accident Had No in the last year Accident in Total the last year Tlﬁ _l l__._ Cellular Phone 23 User (Not Cellular Phone 46 User Use a signiﬁcance level of oz =0.05 to test the claim that occurrences of accidents is not independent of the use of cellular phones. 7. [10 pts] In a morning exit poll of 700 voters done on the election day, 347 indicated they had voted for the Democratic candidate and 323 said they had voted for the Republican candidate. The remaining 30 said they voted for neither of those two candidates. Use this sign test (e. g. Democrat= '+ ’, Republican = ‘-') at the 0.05 significance level to test the claim that more voters voted for the Democratic candidate than the Republican candidate. ...
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MAT122-2005SpringUC - MATH 122 UC FINAL EXAM 9TH MAY 2005...

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