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STAT 235 Homework 9 Problems

Question # 00013428
Subject: Statistics
Due on: 04/25/2014
Posted On: 04/25/2014 04:52 AM

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1. The mean drying time of a brand of spray paint is known to be 90 seconds. The research division of the company that produces this paint contemplates that adding a new chemical ingredient to the paint will accelerate the drying process. To investigate this conjecture, the paint with the chemical additive is sprayed on 15 surfaces and the drying times are recorded. The mean and standard deviation computed from these measurements are 86 and 4.5 seconds, respectively. Assume the measurements constitute a random sample from a normal population. Answer the following questions.
(a) Define ? in the context of this problem.
(b) What is the point estimate for the mean drying time of the spray paint with the new chemical ingredient?
(c) Construct a 98% confidence interval for the mean drying time of the paint with the chemical additive. Is ? included in this interval?
(d) Do these data provide strong evidence that the mean drying time is reduced by the addition of the new chemical? Perform the hypothesis testing (at the significance level ? = .02) by answering the questions arranged in the following.
i. Formulate the null and alternative hypotheses.
ii. State the Type I error and Type II error in the context of the problem and tell why Type I error is
more serious.
iii. State the test statistic and its distribution.
iv. Determine the critical value for ? = .025 and state the decision rule.
v. Calculate the observed value of the test statistic from the data.
vi. State whether H0 is rejected and tell why.
Readings: Section 10.3.

2. Rural and urban students are to be compared on the basis of their scores on a nationwide musical aptitude test. Two random sample of sizes 90 and 100 are selected from rural and urban seventh grade students. The summary statistics from the test scores are
???Sample size
Mean
Standard deviation
Rural Urban
90 100 76.4 81.2 8.2 7.6
Answer the following questions.
(a) Define ?1 and ?2 in the context of the problem.
(b) What is the point estimate for ?1 ? ?2?
(c) Construct a 97% confidence interval for ?1 ? ?2. Is ? included in this interval?
(d) Do these data provide strong evidence that there is a difference in population mean scores between urban and rural students? Perform the hypothesis testing (at the significance level ? = .01) by answering the questions arranged in the following.
i. Formulate the null and alternative hypotheses. ii. State the test statistic and its distribution.
iii. Determine the critical value for ? = .01 and state the decision rule. iv. Calculate the observed value of the test statistic from the data.
v. State whether H0 is rejected and tell why.

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STAT 235 Homework 9 Problems Solution

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Tutorial Preview …8 x 7 xxxxxxx the following xxxxxxxxx (a) Define xx and xx xx the xxxxxxx of the xxxxxxx (b) What xx the xxxxx xxxxxxxx for xx ? ?2?(c) xxxxxxxxx a 97% xxxxxxxxxx interval xxx xx ? xx Is ? xxxxxxxx in this xxxxxxxxxxxx Do xxxxx xxxx provide xxxxxx evidence that xxxxx is a xxxxxxxxxx in xxxxxxxxxx xxxx scores xxxxxxx urban and xxxxx students? Perform xxx hypothesis xxxxxxx xxx the xxxxxxxxxxxx level ? x 01) by xxxxxxxxx the xxxxxxxxx xxxxxxxx in xxx following i xxxxxxxxx the null xxx alternative xxxxxxxxxx xx State xxx test statistic xxx its distribution xxx Determine xxx xxxxxxxx value xxx ? = xx and state xxx decision xxxx xx Calculate xxx observed value xx the test xxxxxxxxx from xxx xxxx v xxxxx whether H0 xx rejected and xxxx why xx xxxxxxx respectively xxx mean scores xxx rural and xxxxx And xxxx xxx construction xxxxxx we can xxx that we xxxx to xxxxx xxxxxxx the xxxxxxxxxx is 0 xx not b) xxx point xxxxxxxx xxxx this xxxxxxx is (76 xxxx 2) = xx 8 xx xxx…
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STAT_235_Homework_9_Problems_Solution.docx (33.79 KB)
Preview: test xxxxxxxxx is,T x Sample mean-hypothesized xxxxxxxxxx SDsample size xxxxxx the xxxx xxxxxxxxxx it xxxxxxx a t xxxxxxxxxxxx with 14 xx The xxxxxxxx xxxxx at x = 0 xxx is,-t0 025,14=-2 xxxxxx the xxxxxxxxx xxxxxxxxx is,Observed xxxx statistic < xxx 025,14=-2 145The xxxx statistic xxxx x Sample xxxxxxxxxxxxxxxxx meanSample SDsample xxxxxxxxxxx 515=-3 443As xx can xxx xxxx the xxxx statistic is xxxxxxx in the xxxxxxxx region xx x Test xxxxxxxxx <Critical value) xxxx we are xxxxxxxxx the xxxx xxxxxxxxxx H0 x Rural and xxxxx students are xx be xxxxxxxx xx the xxxxx of their xxxxxx on a xxxxxxxxxx musical xxxxxxxx xxxx Two xxxxxx sample of xxxxx 90 and xxx are xxxxxxxx xxxx rural xxx urban seventh xxxxx students The xxxxxxx statistics xxxx xxx test xxxxxx areSample sizeMeanStandard xxxxxxxxxxxxxx Urban90 100 xx 4 xx x 8 x 7 6Answer xxx following questions xxx Define xx xxx ?2 xx the context xx the problem xxx What xx xxx point xxxxxxxx for ?1 x ?2?(c) Construct x 97% xxxxxxxxxx xxxxxxxx for xx ? ?2 xx ? included xx this xxxxxxxxxxxx xx these.....
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