# Standard basis

Let D: P5 |-> P5, Where D = d /dx . Find the matrix of the D relative to the standard basis, { 1,x, x^2,x^3,x^4,x^5}.

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#### Solution Summary

This provides an example of finding a matrix relative to a standard basis.

Problems on Basic Statistical Concepts

I need some help on answer these questions with workings: (See attached file for full problem description)

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1) What is the best point estimate of the

a) population parameter?

b) population variance?

2) A sample of 100 elements produced a mean of 48 and a standard deviation

of 8. Find the 99% confidence interval for the population mean. Hint - this is a large sample.

3) A recent study of 28 city residents showed that the mean of the time they had lived at their present address was 9.3 years. The standard deviation of the sample was 2 years. Find the 90% confidence interval of the true mean.

4) A university dean wishes to estimate the average number of hours his part-time instructors teach per week. The standard deviation from a previous study is 2.6 hours. How large a sample must be selected if he wants to be 99% with a maximum error of one hour.

5) An employment counselor found that in a sample of 100 unemployed workers, 65% were not interested in returning to work. Find the 95% confidence interval of the true proportion of workers who do not wish to return to work.

6) A nutritionist wishes to determine, within 3%, the true proportion of adults who do not eat any lunch. If he wishes to be 95% confident that it contains the population proportion, how large a sample will be necessary? A previous study found that 15% of the 125 people surveyed said they did not eat lunch.

7) A tektronics dental X-ray machine bears a label stating that the machine gives radiation dosages with a mean of less then 8 milliroentgens. Sample data consists of 66 randomly selected observations with a mean of 7.13 milliroentgens and a standard deviation of 1.61 milliroentgens. Using a .01 level of significance, test the claim stated on the label.

a. State the claim:

b. Is this a one-tailed test or a two-tailed test?

c. What are the two decisions that can be made in a hypothesis test?

d. In simple terms, describe a Type I error:

e. In simple terms, describe a Type II error:

f. Identify the probability of making a Type I error:

8) The Dengue Fever medication, H76 bears a label indicating the presence of 600 mg of acetaminophen in each fluid ounce of the drug. The FDA randomly selected 75 one-ounce samples and found that the mean acetaminophen content is 579mg and the standard deviation is 20 mg. Using a .01 level of significance, test the claim of Monkey Pharmaceutical Company that the population mean is equal to 600 mg.

a. State the claim:

b.

c. Test Statistic:

d. Decision:

e. Conclusion:

Would you buy this medication? Why or why not?

9) A health club manager claims that members lose an average of 15 pounds during the first six months of membership. A sample of fifteen members of the club showed they lost an average of 11.5 pounds during the first six months of membership with a standard deviation of 2.2 pounds. Test at the 5% significance level if the mean weight loss during the first six months of their membership by all members of this health club is less than 15 pounds.

a. State the claim:

b.

c. Test Statistic:

d. Decision:

e. Conclusion:

10). A department store manager claims that at least 45% of persons who visit this store make a purchase. In a sample of 400 persons who visited this store, 37% made a purchase. Test at the 5% significance level if the claim of the management is true.

a. State the claim:

b.

c. Test Statistic:

d. Decision:

e. Conclusion:

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