Given a sample of variance 127 from a set of nine observations, construct a 95% confidence interval for the population variance
tutor4helpyou1) Given a sample of variance 127 from a set of nine observations, construct a 95% confidence interval for the population variance.
2) An operations manager feels that the output rate of experienced employees is greater than that of new employees but he does not expect the variability in output rates to differ for the two groups. Previous studies indicate that the average unit output per hour for new employees at a particular type of work is 20 units per hour with a variance of 56 units squared. For a group of 20 employees with 5 years’ experience, the average output for this same type of work is 30 units per hour with a sample variance of 28 units squared. Does the variability in output appear to differ at the two experience levels? Test the hypotheses at the .05 significance level.
3) A quality control manager for an automotive firm is concerned with uniformity in the number of defects in cars coming off the assembly line. If one assembly line has significantly more variability in the number of defects, then changes have to be made. The quality control manager has collected the following data:
| Number of Defects | |
Assembly Line 1 | Assembly Line 2 | |
Mean | 10 | 11 |
Variance | 9 | 25 |
Sample Size | 20 | 16 |
Does assembly line 2 have significantly more variability in the number of defects? Test at the .05 significance level.
4) A recruitment firm subjects candidates to interviews by three different executives and then seeks to obtain a consensus evaluation for each candidate. Each executive gives the candidate a positive or a negative rating. The interview results of 100 candidates are as given below:
Possible Positive Ratings from Three Interviews | Number of Candidates Receiving Each of These Ratings |
0 | 18 |
1 | 47 |
2 | 24 |
3 | 11 |
The recruitment manager feels that the interview process can be approximated by a binomial distribution with p = 0.40 (i.e. a 40% chance of any candidate receiving a positive rating on any one interview). Test this hypothesis at the .20 level of significance.
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