# mathematics

**Problems **

- Suppose the historical average work week was 39.2 hours and SD was 4.8 hours as reported by the labor Dept. This year a study of 112 workers showed a mean of 38.5 hours. Test whether the workweek is the same or significantly shorter due to the recession. (Left tail. Ho: M=> 39.2). Use a .02 significance level.
- Critical Value
- What is the appropriate T or Z Statistical
- Practical conclusion

- A Shelloil company executive says that a majority of workers – more than 50% – prefer a 10 hour four day work week over an 8 hour five day work week. Of a 105 worker sample, 67 said they prefer a 10-hour-4-day work-week. At alpha- significance level of .01 does this sample support the executive’s suggestion (right tail)
- Critical Value
- What is the appropriate calculated test statistic T or Z
- Statistical conclusion
- Practical conclusion
- The financial industry Earnings per share last year were $3. This year, earnings per share in 10 financial companies were as follows. Test the hypothesis that this year’s earnings differ from last year – two tail, at alpha (significance level) =.10.

Data 1.92, 2.16, 3.63, 3.16, 4.10, 3.14, 2.20, 2.34, 3.10, 2.38

- Hypothesis being tested – equality of means
- Critical Value
- What is the appropriate T or Z
- Statistical conclusion
- Practical conclusion
- Two Samples: Male and female muscle flexibility were measured and reported as follows. Test the hypothesis of mean equality at .10 level of significance.

Sample mean SD

Male 45 18.64 3.29

Female 31 20.99 2.07

- Hypothesis being tested:

- Critical Value
- What is the appropriate calculated T or Z

- Statistical conclusion
- Practical conclusion

- Sample size: In a 2003, a preliminary study showed that 20% of Americans smoke. At 99% confidence, What would be an appropriate sample size to find out the proportion of American adults who smoke, if you want a margin of error of 2%

- Confidence Interval: A study showed that 110 of 200 people say that their major source of news is TV.
- What would be a 95% confidence interval for the proportion? _____________
- Comment. Is this narrow range? Wide? Who uses this information? ________
- Confidence Interval :A sample of 80 Forbes magazine readers shows an average household income of 119 K and a standard deviation of 30k.
- What would the 90% confidence interval be? _________________

- What is the 95% confidence interval? Wider or narrower? ________

- Confidence interval :On a scale of 1-100, a sample of 10 restaurant guests showed a mean customer satisfaction level of 71 points and a standard deviation of 5 points. At 90%, what would be the confidence interval of the mean?

- The following data based on a study by the American heart association on how age, blood pressure, and smoking can predict the risk of a stroke.

risk | 12 | 24 | 13 | 56 | 28 | 51 | 18 | 31 | 37 | 15 |

Age | 57 | 67 | 58 | 86 | 59 | 76 | 56 | 78 | 80 | 78 |

Pressure | 152 | 163 | 155 | 177 | 196 | 189 | 155 | 120 | 135 | 98 |

smoker | N | N | N | Y | N | Y | Y | N | Y | N |

- Write the multiple regression equation.
- What areR
^{2 }, P-value-, T , F and what do they mean?

- Based on your model, What is the risk level of a 50 years old smoker whose average Blood pressure is 135?

**d.****Explain its statistical significance.**

- Drop one less significant variable and try again. Is it a better model?In what way? Explain.

- In the clinical trials of the allergy medicine Clarinex, 50 out of 1655 individuals reported having dry mouth. In the placebo control group, 31 out of 1652 reported having a dry mouth as a side effect. Test the equality of proportions VS the alternative hypothesis that Clarinex causes dry mouth – at .05 significance level.
- Hypothesis being tested?
- Critical Value
- What is the appropriate T or Z

- Statistical conclusion
- Practical conclusion

- Children attention span in seconds to TV commercials was measured for clothes, food and toys. Data as follows.

clothes | 26 | 21 | 43 | 35 | 28 | 31 | 17 | 31 | 20 | |||

food | 45 | 48 | 43 | 53 | 47 | 42 | 34 | 43 | 57 | 47 | 44 | 54 |

toys | 60 | 51 | 43 | 54 | 63 | 53 | 48 | 58 | 47 | 51 | 51 |

- What do you conclude about the variation in these three types of commercials?
- Conduct three pairwise comparisons (as we did in ch 11 – compare each pair of means – use Z. What are the conclusions?

- Eight operating rooms were tested to see if a bacterial soap has reduced the contamination rates. The data shows the contamination in each room the year before and the year after using the soap. What do you conclude at .10 significance level

Before: 6.6 6.5 9 10.3 11.2 8.1 6.3 11.6

After: 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2

- Hypothesis being tested: M1=M2? Or should it be a one tail test?
- Critical Value
- What is the appropriate calculated T or Z

- Statistical conclusion
- Practical conclusion. Does the contamination significantly change?