Homework #7 Problems
Do the following problems from Chapter 7 using the modified statements given below:
7.2: 3, 8, 11; 7.3: 1, 5, 6
7.2.3) A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5. psi and standard deviation 3.5 psi. What is the standard deviation of the sample mean when the sample size is (a) n = 10 and (b) n = 45.
7.2.8) Scientists at the Hopkins Memorial Forest in Western Massachusetts have been collecting meteorological and environmental data in the forest for more than 100 years. In the past few years, sulfate content in water samples from Birch Brook has averaged 7.5 mg/L with a standard deviation of 1.5 mg/L.
- What is the standard error of the sulfate in a collection of 15 water samples?
- If 15 students measure the sulfate in their samples, what is the probability that their average will be between 5.75 and 7.35 mg/L?
- What do you need to assume for the probability calculated in (b) to be accurate?
7.2.11) Like hurricanes and earthquakes, geomagnetic storms are natural hazards with possible severe impact on the Earth. Sever storms can cause communication and utility breakdons, leading to possible blackouts. The National Oceanic and Atmospheric Administration beams electron and proton flux data in various energy ranges to various stations on the Earth to help forecast possible disturbances. The following 25 readings of proton flux in the 47-68 kEV range (units are in p.cm2 –sec-srer-MeV) on the evening of December 28, 2011:
2300 2310 2020 10810 2180 3340 5680 2560 3320 11780 2000 3410 10600 7350 2140 3210 2010 2810 3510 10190 8540 9500 2250 7750 2220
- Find a point estimate of the standard deviation of the proton flux in this time period.
- Find the estimate of the mean proton flux in this time period.
- Find the point estimate of the median proton flux in this time period.
- Find an estimate of the standard error of the estimate in Part (b).
7.3.1) A computer software package calculated some numerical summaries of a sample of data. The results are displayed here:
| Variable | n | Sample Mean ( | Estimate of Std, Error (SE) of Mean | Sample Std. Dev (S) | Sample Variance (S2) | Sum ( | Sum of Squared Deviations
|
| X | 1.527525 | 3.741657 | 90 | 70 |
- Fill in the missing entries.
- What is the estimate of the mean of the population from which this sample was drawn?
- What is the estimate of the population variaance from which this sample was drawn?
- What is the estimate of the population standard deviation from which this sample was drawn?
7.3.5) Suppose that are estimators of θ. We know that
.
- Which do you prefer between the first two estimators?
- Compare these three estimators. Which do you prefer? Why?
7.3.6) Data on pull-off force (pounds) for connectors used in an automobile engine application are as follows: 79.0, 75.1, 78.3, 74.5, 73.8, 75.1, 77.5, 77.8, 73.3, 74.6, 75.0, 74.4, 74.7, 75.4, 72.8, 73.6, 74.1, 78.2, 75.6, 76.7, 74.8, 78.1, 75.6, 76.7, 75.4, 76.0.
- Calculate a point estimate of the pull-off force of all connectors in the population. State which estimator you used and why?
- Calculate a point estimate of the median pull-off force.
- Calculate point estimates of the population variance and the population standard deviation.
- Calculate the standard error of the point estimate found in part (a). Interpret the standard error.
- Calculate a point estimate of the proportion of all connectors in the population whose pull-off force is less than 75 pounds.
