# OSU BUSMGT 2320 - DirectFileTopicDownload (4 pages)

Previewing page*1*of 4 page document

**View the full content.**## DirectFileTopicDownload

Previewing page
*1*
of
actual document.

**View the full content.**View Full Document

## DirectFileTopicDownload

0 0 562 views

- Pages:
- 4
- School:
- Ohio State University
- Course:
- Busmgt 2320 - Decision Sciences: Statistical Techniques

**Unformatted text preview:**

Recitation Practice Problems One Sample Inference and p 1 Which of the following statements is false A The t distribution is symmetric about zero B The t distribution is more spread out than the standard normal distribution C As the degrees of freedom get smaller the t distribution s dispersion gets smaller D The t distribution is mound shaped 2 For a sample of size 20 taken from a normally distributed population with standard deviation equal to 5 a 90 confidence interval for the population mean would require the use of A t 1 328 B t 1 729 C z 1 96 D z 1 645 3 For a sample of size 20 taken from a normally distributed population with unknown population standard deviation a 90 confidence interval for the population mean would require the use of A t 1 328 B t 1 729 C z 1 96 D z 1 645 4 The lengths of steel rods produced by a shearing process can be modeled with a Normal distribution A random sample of 8 rods is selected and the following lengths are measured 10 9 9 10 10 1 9 9 9 8 10 10 3 Construct a 98 confidence interval to estimate the population mean length of the rods produced by the process One Sample T Length Variable Length N 8 Mean 10 0000 StDev 0 1512 SE Mean 0 0535 98 CI 9 8398 10 1602 5 Data contained in The National Survey of Student Engagement The College Student Report 2009 showed that 39 of the first year college students in a sample of 159 949 participated in community service or volunteer work a Find the margin of error using a 99 confidence level Answer 0 0031 b Here are some facts from the report that summarizes the survey The students were from 617 four year colleges and universities The response rate was 36 Institutions paid a participation fee of between 1800 and 7800 based on the size of their under graduate enrollment Discuss these facts as possible sources of error in this study How do you think these errors would affect the margin of error calculated in part a Recitation Practice Problems One Sample Inference and p 6 Senator Fogbound has vague information that suggests that at least a third of the registered voters in his state support a proposed piece of environmental legislation He would like a more specific estimate of the proportion though He does not want more than a 3 percentage point error in the estimate He has asked you to conduct a survey to obtain this estimate It costs 15 00 per person surveyed and he has allocated 3000 for sampling costs a What is the maximum level of confidence attainable for the confidence interval Answer 63 18 b What budget is needed in order to limit the margin of error to 3 percentage points and have 95 confidence Answer n 949 Budget 14 235 7 The diameter of 4 5 inch discs is normally distributed Periodically quality control inspectors at Dallas Diskettes randomly select a sample of nine diskettes If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment otherwise the punching process continues The last sample showed a mean of 4 54 inches Does this provide statistically significant evidence at the 5 s significance level that the punch should be shut down for adjustment a Assume the population standard deviation is 0 06 One Sample Z Test of mu 4 5 vs not 4 5 The assumed standard deviation 0 06 N 9 Mean 4 5400 SE Mean 0 0200 95 CI 4 5008 4 5792 Z 2 00 P 0 046 b Assume the population standard deviation is unknown and the sample standard deviation is observed to be 0 06 One Sample T Test of mu 4 5 vs not 4 5 N 9 Mean 4 5400 StDev 0 0600 SE Mean 0 0200 95 CI 4 4939 4 5861 T 2 00 P 0 081 Recitation Practice Problems One Sample Inference and p 8 A television station claims that 30 or more of the residents of households in the viewing area watches their 11 00 news To test the station s claim an advertiser randomly selects 50 households and finds that the residents in 14 of these households watch this television station s 11 00 news broadcast Show that the sample evidence is not strong enough at the 5 significance level to refute declare false the television station s claim StatTools Results Hypothesis Test Proportion Category Sample Size Sample Proportion Hypothesized Proportion Alternative Hypothesis Standard Error of Sample Proportion z Test Statistic p Value Minitab Results Watch 11 PM News 1 50 0 280 0 3 0 3 0 065 0 3086 0 3788 Test and CI for One Proportion Test of p 0 3 vs p 0 3 Sample 1 X 14 N 50 Sample p 0 280000 95 Upper Bound 0 384445 Z Value 0 31 P Value 0 379 Using the normal approximation a Rejection Region Method b P value Method c Confidence Interval Method 9 A 95 confidence interval to estimate the population proportion that has a margin of error no larger than 0 03 is desired How large must the sample size be if the population proportion is assumed to be each of the following Proportion Work n 0 10 385 0 25 801 0 40 1025 0 50 1068 0 60 1025 0 75 801 0 90 385 Recitation Practice Problems One Sample Inference and p 10 Bursaries are loans made to students who need the money to support themselves while attending universities and colleges The loans are made by banks that are guaranteed repayment by the government A government auditor wanted to know the status of the loans made to students at one university She randomly sampled 188 of the 2 684 loans that are outstanding The total amounts owing were recorded Estimate with 90 confidence the total outstanding amount of the loans made to students at the university Conf Intervals One Sample Sample Size Sample Mean Sample Std Dev Confidence Level Mean Degrees of Freedom Lower Limit Upper Limit Amounts Data Set 1 188 12939 84 4139 18 90 0 187 12440 81 13438 86 Approximate Answer 33 391 134 36 069 900 Better answer uses the finite population correction factor 33 433 267 36 027 794 The distribution of loan amounts is likely skewed Why is this solution reliable nonetheless 11 Suppose the following hypotheses are tested H0 2 5 Ha 2 5 The P value for the test is 0 022 If the same sample data are used which of the following is true A A 95 confidence interval for will include the value 2 5 B A 95 confidence interval for will include the value 0 C A 99 confidence interval for will include the value 2 5 D A 99 confidence interval for will include the value 0 12 A null hypothesis was rejected at the 0 10 level of significance If the significance level is changed to 0 05 and everything else …

View Full Document