Archive for July, 2015

Problem 909

Consider an experiment designed to determine the effectiveness of a new drug. The drug is given to participants in the treatment group, while participants in the control group receive a placebo. For the set of results described, discuss whether there appears to be evidence that the treatment is effective.

75% of those in the treatment group showed improvement; 26% of those in the placebo group showed improvement.

 

Solution:-

 

Is there good evidence that the treatment is effective?

Yes

 

 

Problem 908

 

Consider an experiment designed to determine the effectiveness of a new drug. The drug is given to participants in the treatment group, while participants in the control group receive a placebo. For the set of result described, discuss whether there appears to be evidence that the treatment is effective.

82% of those in the treatment group showed improvement; 18% of those in the placebo group showed improvement.

 

Solution:-

 

In this experiment there are two groups. The first group is the treatment group. The treatment group receives the real treatment. Therefore, a higher percentage of those that show improvement in this group shows that the treatment is effective.

The second group is the placebo group. The placebo group lacks the active ingredients of the treatment being tested. This is to keep the placebo effect from affecting the results. The placebo effect refers to the situation in which patients improve simply because they believe they are receiving a useful treatment. Therefore, a lower parentage of those that show improvement in this group shows that the treatment is effective.

Therefore, since the treatment group had the higher percentage of improvements, there is good evidence that the treatment is effective.

 

Problem 907

Identify the sampling method as simple random sampling, systematic sampling, convenience sampling, or stratified sampling.

A computer randomly selects 700 names form a list of all registered voters. Those selected are surveyed to predict who will win the election for Mayor.

 

Solution:-

 

Simple random sampling

We choose a sample of items in such a way that every sample of a given size has an equal chance of being selected.

 

Problem 906

 

Identify the sampling method as simple random sampling, systematic, convenience sampling, or stratified sampling.

An IRS (Internal Revenue Service) auditor randomly selects for audits 80 taxpayers in each of the filing status categories: single, head of household, married filing jointly, and married filing separately.

 

Solution:-

 

Stratified sampling

We use this method when we are concerned about differences among subgroups, or strata, within a population. We first identify the subgroups and then draw a simple random sample within each subgroup. The total sample consists of all the samples from the individual subgroups.

 

 

Problem 905

Simple random sampling:-

We choose a sample of items in such a way that every sample of a given size has an equal chance of being selected.

 

Systematic sampling:-

We use a simple system to choose the sample, such as selecting every 10th or every 50th member of the population.

 

Convenience sampling:-

We use a sample that is convenient to select, such as people who happen to be in the same classroom.

 

Stratified sampling:-

We use this method when we are concerned about differences among subgroups, or strata, within a population. We first identify the subgroups and then draw a simple random sample within each subgroup. The total sample consists of all the samples from the individual subgroups.

 

Problem 904

For the study described below, identify the population parameter.

A researches is interested in the level of stress among emergency-room nurses in the U.S. 275 emergency-room nurses were interviewed to determine their level of stress. Each nurse was assigned a stress rating based on his answers to a number of questions. The average stress rating for the 275 nurses was determined.

 

Solution:-

 

The average stress rating for all emergency-room nurses in the U.S

 

Problem 903

For the study described below, identify the sample.

A bank manager wants to know the average amount of time customers of his bank have to wait in line. 400 customers were polled and asked their average wait time at the bank. 35 of the 400 were extremely dissatisfied with the amount of time they had to wait in line in recent months.

 

Solution:-

 

The 400 customers polled.

 

 

Problem 902

For the study described below, identify the population.

A manufacturer of light bulbs wants to determine the average lifetime of its 75-watt light bulbs. Among 120 randomly selection 75-watt light bulbs, the average lifetime was 1007 hours.

 

Solution:-

 

All 75-watt light bulbs manufactured by the company.

 

Problem 901

Given the annual interest rate and the compounding period, find I, the interest rate per compounding period.

12% compounded monthly.

 

Solution:-

 

The interest rate per compounding period is i = \frac{r}{m} where r is the annual nominal rate and m is the number of compounding periods per year.

The interest is compounded monthly, so the compounding period is one month. There  are 12 months in one year.

m= 12

Divide the annual rate by the number of periods per year.

i= \frac{r}{m}

= \frac{12}{12}

=1 percent

The interest rate per compounding period is 1 percent  per month.

 

Problem 900

 

Use the continuous compound interest formula to find the indicated  value.

P = 4000, r = 4.35%, t = 5 years , A = ?

 

Solution:-

 

If a principal P is invested at an annual rate r (expressed as a decimal) compounded continuously, then the amount A in the account at the end of t  years is given by the following formula.

A = Pert

The values for P, r, and t are given. However, r must be converted to a decimal.

P = 4000 , r = 0.0435, t= 5

Substitute these values into the formula and simplify, rounding to the nearest cent.

A = Pert

= 4000e(0.0435*5)

= 4971.86

The amount in the account after 5 years is about 4971.86.