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Lett0 be a specific value of t. Use Table III in Appendix D to findt0 values such that the following statements are true.

a. (tt0)=0.025where df=11

b.(tt0)=0.01 wheredf=9

c.(tt0)=0.005 wheredf=6

d.(tt0)=0.05 wheredf=18

Short Answer

Expert verified
  1. .The value oft0 fortt0=0.025wheredf=11 is 2.201
  2. The value oft0 fortt0=0.01 wheredf=9is 2.821
  3. The value oft0 fortt0=0.005wheredf=6 is 3.707

4. The value oft0 fortt0=0.05 wheredf=18 is 1.734

Step by step solution

01

Calculating the value of t0 Such that Ρ(t≥t0)=0.025

Giventt0=0.025wheredf=11

By using t- distribution table, we will see the row with 11 degrees of freedom and column corresponds to=0.025 in the one-tail.

Hence from the critical values we get t0.025,11=2.201

02

Calculating the value t0 of Such that Ρ(t≥t0)=0.01

Given(tt0)=0.01wheredf=9

By using t- distribution table, we will see the row with 9 degrees of freedom and column corresponds to=0.01 in the one-tail.

Hence from the critical values we gett0.01,9=2.821

03

Calculating the value of t0 Such that Ρ(t≥t0)=0.005

Giventt0=0.005wheredf=6

By using t- distribution table, we will see the row with 6 degrees of freedom and column corresponds to=0.005 in the one-tail.

Hence from the critical values we gett0.005,6=3.707

04

Calculating the value of t0 Such that Ρ(t≥t0)=0.05

Giventt0=0.05 wheredf=18

By using t- distribution table, we will see the row with 18 degrees of freedom and column corresponds to=0.05 in the one-tail.

Hence from the critical values we get t0.05,18=1.734.

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Most popular questions from this chapter

Unethical corporate conduct. How complicit are entrylevel accountants in carrying out an unethical request from their superiors? This was the question of interest in a study published in the journal Behavioral Research in Accounting (July 2015). A sample of 86 accounting graduate students participated in the study. After asking the subjects to perform what is clearly an unethical task (e.g., to bribe a customer), the researchers measured each subject鈥檚 intention to comply with the unethical request score. Scores ranged from -1.5 (intention to resist the unethical request) to 2.5 (intention to comply with the unethical request). Summary statistics on the 86 scores follow: x=2.42,s=2.84.

a. Estimate , the mean intention to comply score for the population of all entry-level accountants, using a 90% confidence interval.

b. Give a practical interpretation of the interval, part a.

c. Refer to part a. What proportion of all similarly constructed confidence intervals (in repeated sampling) will contain the true value of ?

d. Compute the interval, x2s. How does the interpretation of this interval differ from that of the confidence interval, part a?

Scallops, sampling, and the law. Interfaces (March鈥揂pril 1995) presented the case of a ship that fishes for scallops off the coast of New England. In order to protect baby scallops from being harvested, the U.S. Fisheries and Wildlife Service requires that 鈥渢he average meat per scallop weigh at least 136 of a pound.鈥 The ship was accused of violating this weight standard. Author Arnold Barnett lays out the scenario:

The vessel arrived at a Massachusetts port with 11,000 bags of scallops, from which the harbormaster randomly selected 18 bags for weighing. From each such bag, his agents took a large scoopful of scallops; then, to estimate the bag鈥檚 average meat per scallop, they divided the total weight of meat in the scoopful by the number of scallops it contained. Based on the 18 [numbers] thus generated, the harbormaster estimated that each of the ship鈥檚 scallops possessed an average of 139 of a pound of meat (that is, they were about seven percent lighter than the minimum requirement). Viewing this outcome as conclusive evidence that the weight standard had been violated, federal authorities at once confiscated 95 percent of the catch (which they then sold at auction). The fishing voyage was thus transformed into a financial catastrophe for its participants. The actual scallop weight measurements for each of the 18 sampled bags are listed in the table below. For ease of exposition, Barnett expressed each number as a multiple of of a pound, the minimum permissible average weight per scallop. Consequently, numbers below 1 indicate individual bags that do not meet the standard. The ship鈥檚 owner filed a lawsuit against the federal government, declaring that his vessel had fully complied with the weight standard. A Boston law firm was hired to represent the owner in legal proceedings, and Barnett was retained by the firm to provide statistical litigation support and, if necessary, expert witness testimony.

0.93

0.88

0.85

0.91

0.91

0.84

0.90

0.98

0.88

0.89

0.98

0.87

0.91

0.92

0.99

1.14

1.06

0.93

  1. Recall that the harbormaster sampled only 18 of the ship鈥檚 11,000 bags of scallops. One of the questions the lawyers asked Barnett was, 鈥淐an a reliable estimate of the mean weight of all the scallops be obtained from a sample of size 18?鈥 Give your opinion on this issue.
  2. As stated in the article, the government鈥檚 decision rule is to confiscate a catch if the sample mean weight of the scallops is less than 136 of a pound. Do you see any flaws in this rule?
  3. Develop your own procedure for determining whether a ship is in violation of the minimum-weight restriction. Apply your rule to the data. Draw a conclusion about the ship in question.

A random sample of size n = 225 yielded p^= .46

a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p? Explain.

b. Construct a 95% confidence interval for p.

c. Interpret the 95% confidence interval.

d. Explain what is meant by the phrase 鈥95% confidence interval.鈥

Material safety data sheets. The Occupational Safety &Health Administration has required companies that handle hazardous chemicals to complete material safety datasheets (MSDSs). These MSDSs have been criticized for being too hard to understand and complete by workers. A

study of 150 MSDSs revealed that only 11% were satisfactorily completed (Chemical & Engineering News, February7, 2005).

a. Give a point estimate of p, the true proportion of MSDSs that are satisfactorily completed.

b. Find a 95% confidence interval for p.

c. Give a practical interpretation of the interval, part b.

FindZ/2for each of the following:

a.= .10

b.= .01

c.= .05

d.= .20

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