Probability Quiz - Statistics Assignment Help

Assignment Task

Quiz

1 Why is the only one table of the normal distribution (such as table provided in class) is needed to find any probability under the normal curve?

2 Why do the individual observations have to be converted to standardized normal ordered values in order to develop a normal probability plot?

3 Why does the standard error of the mean decreases as the sample size ‘n’ increases?

4 Why does the sampling distribution of the mean follow a normal distribution for a large sample size even though the population may not be normally distributed?

5 What is the difference between a probability distribution and a sampling distribution?

6 A market researcher states that she has 95% confidence that the true mean monthly sales of a product are between Rs.1, 70,000 and Rs.2, 00,000. Explain the meaning of this statement.

7 A manufacturer of computer paper has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 11 inches and the standard deviation of the length is known to be 0.02 inch. At periodic intervals, samples are selected to determine whether the mean paper length is still equal to 11 inches or whether something has gone wrong in the production process to change the length of the paper produced. If such a situation has occurred, corrective action is needed. Suppose a random sample of 100 sheets is selected, and the mean paper length is found to be 10.998 inches. Set up a 90%, 95%, 99% confidence interval estimate of the population mean paper length.

8 A manufacturing company produces electric insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing in high-powered labs is carried out to determine how much force is required to break the insulators. Force is measured by observing how many pounds must be applied to the insulator before it breaks. Thirty observations from this experiment are summarized in table. Set up a 95% confidence interval estimate of the population mean force required to break the insulator.

Suppose you want to estimate the population mean force required to break the insulator within ± 25 pounds of the true value and you want to be 95% confident of correctly estimating the true mean. On the basis of a study taken the previous year, you believe that the standard deviation is 100 pounds. Find the sample size needed.

9 The operations Manager for a large newspaper wants to determine the proportion of newspapers printed that have a nonconforming attribute, such as excessive rub-off, improper page setup, missing pages, and duplicate pages. The operations manager determines that a random of 200 newspapers should be selected for analysis. Suppose that, of this sample of 200, thirty-five contain some type of 2 non-conformances. If the operations manager wants to have 90% confidence of estimating the true proportion, set up the confidence interval estimates.

10 Specify the null hypothesis and alternative hypothesis of the following cases.

a. Excel Ltd wants to confirm a supplier’s claim that the maximum resistance in a wiring circuit is less than 150 Ohms.

b. An investigator wants to establish the research department’s claim that a new filament will increase the mean bulb life to more than 4000 hours.

c. Joint Parliamentary Committee (JPC) wants to test the claim of Pepsi/Coke that amount of pesticides in the cold drinks is tolerable.

d. A PhD student at Mech. Eng. Department claims that fuel developed by him is an efficient alternative to CNG (Compressed Nitrogen Gas).

e. In response to a RTI query, Architecture Department wants to assert that IITR does not commit any gender bias in selecting candidate for UG Architecture admission.

11 Take real life example. Formulate your own null hypothesis. Highlight the procedure to accept/reject the null hypothesis. Be as specific as possible.

12 Interpret the meaning of “statistical significant” in your own words with real life examples.

13 The quality-control manager at a light-bulb factory needs to determine whether the mean life of a large shipment of light-bulbs is equal to the specified value of 375 hours. The process standard deviation is known to be 100 hours. A random sample of 64 light-bulbs indicates a sample mean life of 350 hours.

a. State the null and alternative hypotheses.

b. At the 0.05 level of significance is there evidence that the mean life is different from 375 hours?

c. Compute the p-value and interpret its meaning,

d. Set up a 95% confidence interval estimate of the population mean life of the light-bulbs.

e. Compare the results of (b) and (d) what conclusions do you reach?

14 The dean of Students at NITC advises to NRI-Parents of incoming students about the cost of textbooks during a typical semester. A sample of 100 students enrolled in the college indicates a sample mean cost of $315.40 with a sample standard deviation of $43.20.

a. Using the 0.10 level of significance, is there evidence that the population mean is above $300?

b. What is your answer in (a) if the standard deviation is $75 and the 0.05 level of significance is used?

c. What is your answer in (a) if the sample mean is $305.11 and the sample standard deviation is S43.20?

15 A certain type of yarn is manufactured under specifications that the mean tensile strength must be 20 pounds. A random sample of 16 specimens yields a mean tensile strength of 18 pounds and a standard deviation of 3.2 pounds. Can we conclude from these data that mean tensile strength of the population is less than 20 pounds?

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