Q: Suppose a new treatment for a certain disease is given to a sample of 200 patients. The treatment was successful for 164 of the patients. Assume that these patients are representative of the population of individuals who have this disease. Calculate a 98% confidence interval for the proportion successfully treated. (Round the answers to three decimal places.)

A: ___ to ___

For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fall independently of each other and that each component has a 0.21 probability of failure.

(A) Would it be unusual to observe one component fail? Two components?
Fill in blanks:
It (would,would not) be unusual to observe one component fail, since the probability that one component fails,___is, (less,greater) than 0.05. It (would not, would) be unusual to observe two components fail, since the probability that two components fail ____, is (greater,less) than 0.05

The following ratings (R) and observed times (OT) represent the elements from question 1. Using the ratings (R) given below for each observation, determine the normal time (NT) for each element. Using the PD&F allowance factor you developed above from question 1, complete the summary and calculate the elemental standard times for each element. Times are in seconds.

A template (which is optional) is available in the course content page, under the Test 3 module.

Q#1

The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.10 years and a standard deviation of 2.00 years. Random samples of size 12 are drawn from the population and the mean of each sample is determined. Round the answers to the nearest hundredth.

Q#2

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be less than 12.1 ounces. Find the probability if the sample is just 1 cup.

Here is a census for an apportionment problem in a hypothetical country comprised of four states. • State of Ambivalence: 8,000; • State of Boredom: 9,000; • State of Confusion: 24,000; • State of Depression: 59,000. (100,000 total) Assume that the house has h = 10 seats to apportion to these four states. What apportionment is determined by the method of: Hamilton, Adam, Jefferson, Webster.

Soma recorded in the table the height of each player on the basketball team

Construct a normal probability distribution curve for this population! Indicate the number for the mean, 1SD, 2SD and 3SD (both sides of the mea) (1+ 6*0.5=4p)

1. A random sample of 4040 cars owned by students had a mean age of 7.37.3 years and a standard deviation of 3.73.7 years, while a random sample of 2828 cars owned by faculty have a mean age of 5.85.8 years and a standard deviation of 3.53.5 years.
   Use a 0.10.1 significance level to test the claim that, on average, cars owned by students are older than cars owned by faculty.
The test statistic is ______________
The p-value is    _______________

2. Ten randomly selected people took IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below.

Calculate (Test B - Test A) to find the differences. Use a 0.010.01 significance level to test the claim that people do better on the second test than they do on the first.

(b) The test statistic is ___________

(c) The p-value is _______________

3. 2.38866e-05
Jaylon thinks that there is a difference in quality of life between rural and urban living. He collects information from obituaries in newspapers from urban and rural towns in Kansas to see if there is a difference in life expectancy. A sample of 20 people from rural towns give a life expectancy of xr¯=80.9xr¯=80.9 years with a standard deviation of sr=6.5sr=6.5 years. A sample of 30 people from larger towns give xu¯=72.4xu¯=72.4 years and su=5.3su=5.3 years. Does this provide evidence that people living in rural Kansas communities have, on average, different life expectancy than those in more urban communities? Use a 5 % level of significance. Let uu represent urban and rr represent rural.

(b) The test statistic is ________________

(c) The p-value is ___________________

Do workers prefer to buy lunch rather than pack their own lunch? A survey of employed Americans found that 75% of the 18 to 24 year-olds, 77% of the 25 to 34 year-olds, 72% of the 35 to 44 year-olds, 58% of the 45 to 54 year-olds, 57% of the 55 to 64 year-olds, and 55% of the 65 + year-olds buy lunch throughout the workweek. Suppose the survey was based on 200 employed Americans in each of six age groups.

a. At the 0.05 level of significance, is there evidence of a difference among the age groups in the preference for buying lunch?

b. Determine the p-value in (a) and interpret its meaning.

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.

Construct a 95% confidence interval for the population mean worth of coupons.  Use a critical value of 2.16 from the t distribution.

You randomly select 20 coffee shops and measure the temperature of the coffee sold at each. The sample mean temperature is 162.0ºF with a sample standard deviation of 10.0ºF. Assume the temperatures are approximately normally distributed. Find the test statistic to test if population average temperature of the coffee is different than 163.5 F.

Solve using R

Either copy & paste each answer from your data sheet, or round your answers to two decimal places where applicable.

Mean

Standard Error

Median

Mode  (report #N/A if no mode)

Standard Deviation

Sample Variance

Kurtosis

Skewness

Range

Minimum/smallest

Maximum/Largest

Sum

Count

Did you notice the mistake in the video while using the data analysis tool? The data range to B1:B100 was selected instead of B1:B101 so there were only 99 values for the Count when the data analysis tool ran. Be sure not to make the same mistake.

The NBS television network earns an average of $400,000 from a hit show and loses an average

of $100,000 on a flop. Of all shows reviewed by the network, 25% turn out to be hits and 75%

turn out to be flops. For $40,000, a market research firm will have an audience view a pilot of a

prospective show and give its view about whether a show will be a hit or a flop. If a show is

actually going to be a hit, there is a 90% chance that the market research firm will predict the

show to be a hit. If the show is actually going to be a flop, there is an 80% chance that the

market research firm will predict the show to be a flop. Determine how the network can

maximize its expected profits by doing the following:

a. Construct the decision tree.

b. What would be the expected profit if the market research firm is hired?

A. According to an airline, flights on a certain route are NOT on time 15% of the time. Suppose 10 flights are randomly selected and the number of NOT on time flights is recorded. Find the probability of the following question. At least 3 flights are not on time.

B. According to an airline, flights on a certain route are NOT on time 15% of the time. Suppose 10 flights are randomly selected and the number of NOT on time flights is recorded. Find the probability of the following question. At the most 8 flights are on time.

c. According to an airline, flights on a certain route are NOT on time 15% of the time. Suppose 10 flights are randomly selected and the number of NOT on time flights is recorded. Find the probability of the following question. In between 6 and 9 flights are on time.

Consider the following all-integer linear program:

1. Solve the LP Relaxation of this problem.
   The optimal solution to the LP Relaxation is x₁ = ___, x₂ = .____________
   
   Its value is ___________
2. Find the optimal integer solution.
   The optimal solution to the LP Relaxation is x₁ = _____x₂ = __________
   Its value is _______