Confidence Intervals for Means

Complete each of the following calculations by providing the correct formula and values that you are using for each problem.

1) A sample size of n = 120 produced the sample mean of ? ̅ = 24.3. Assuming the population standard deviation ? = 5.2, compute a 99% confidence interval for the population mean. Interpret the confidence interval.


2) Assuming the population standard deviation ? = 4, how large should a sample be to estimate a population mean with a margin of error of 0.2 for a 95% confidence interval?


3) The manager of a plant would like to estimate the mean amount of time a worker takes to complete a specific task. Assume the population standard deviation for this task is 4.1 minutes.

a. After observing 70 workers completing the same type of task, the manager calculated the average time to be 12.7 minutes. Construct a 90% confidence interval for the mean task time. Interpret the confidence interval.

b. How large a sample size n should he observe to decrease the margin of error to 0.5 minutes for the 90% interval?

4) A sample of 25 was selected out of a specific population with mean equal to 18.4 and sample standard deviation of 3.6. Construct a 95% confidence interval for the mean of the population. Interpret the confidence interval.


5) A group of students were randomly selected to participate in a study that compared the female grades to the male grades for a specific test. There were 15 females with a mean grade of 94.3 and sample standard deviation of 3.6. There were 12 males with a mean grade of 90.6 and sample standard deviation of 5.1. Construct a 90% confidence interval for the difference between the females’ and males’ test grades. Interpret the confidence interval.

Use the following scenario and data to answer questions 12.1 – 12.5. A researcher is interested in how many days it takes athletes to recover from jet lag when they have had to fly a long distance. It is commonly known that traveling east (moving “ahead” in time) leads to more serious jet lag than travelling west. The researcher finds 18 professional athletes who just travelled a long distance; six stayed in the same time zone, six travelled west, and six travelled east.

12.1 Calculate the sum of squares for each treatment condition (SHOW WORK)

SS_w =                                         SS_e =                                          SS_s =

12.2 What is the value of N in this experiment?

12.3 What number should appear in the denominator of your F-ratio? (I want the actual number, not the name of it)

12.4 What number should appear in the numerator of your F-ratio? (I want the actual number, not the name of it) (SHOW WORK)

12.5 Do the data show a significant difference in jet lag depending on the direction of travel? Use a two-tailed test and alpha = .05.

What are the two hypotheses of the F test?

In order for the F test to be significant, do you need a high or a low value of R2? Why? How are the standardized regression coefficients computed?

How are they useful?

What are their measurement units?

Please provide several examples of a negative correlation coefficient.

Explain why the results of a presidential election poll can sometimes lead to an inaccurate conclusion about who will win the election. Hint: Chapter 6 should help you understand this.

9. Police plan to enforce speed limits by using radar traps at four different locations within the city limits. A person who is speeding on his/her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations (location 1, location 2, location 3, and location 4, respectively). The radar traps at each of the locations (location 1, location 2, location 3, and location 4, respectively) will be operated 40%, 30%, 20%, and 30% of the time. If a randomly selected person received a speeding ticket on his/her way to work, what is the probability that he/she passed through the radar trap located at location 1? (10 points)

Hint: Consider the following five events:

A: a speeding person receives a speeding ticket (note: a speeding person will receive a speeding ticket if the person passes through the radar trap when operated.)

B₁: a speeding person passing through location 1,

B₂: a speeding person passing through location 2,

B₃: a speeding person passing through location 3,

B₄: a speeding person passing through location 4.

A deck consists of 72 cards with 9 suits labelled ? to ? and numbered ranks from 1 to 8. That is, there are 8 cards of each suit and 9 cards of each rank. What is the probability of it being suit C or having rank 6?

Use the following information for Questions 1-3: At Regan's Tomato Heaven Farm, the yield per acre, measured in bushels of tomatoes, is known to follow a Normal Distribution with variance σ2 = 225.

1. A random sample is obtained with the following results:

n=16.

Sample mean X-Bar: 56.

Provide a test of null hypothesis H0: μ = 48 versus the alternative hypothesis HA: μ ≠ 48 with α = 0.05.

a. Calculated Z-Score =

b. Z-Critical =

c. Conclusion (Reject H0/Fail to Reject H0)

3. Another random sample is obtained with the following results:

n=36.

Regan would like to conduct a test of null hypothesis H0: μ = 55 versus the alternative hypothesis HA: μ < 55 with α = 0.01

a. Z-Critical =

b. X-Bar Critical. That is, at what value of X-Bar woud you reject H0:

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:

If the Edwards production plan for the next period includes 1000 units of component 1 and 775 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? Round your answers to the nearest whole number. If your answer is zero, enter "0".

What is the total purchase cost for the components? Round your answer to the nearest dollar.

$  

Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 68 wpm and standard deviation 17 wpm.

What is the probability that a randomly selected typist's speed is at most 68 wpm?

What is the probability that a randomly selected typist's speed is less than 68 wpm?

What is the probability that a randomly selected typist's speed is between 34 and 85 wpm? (Round your answer to four decimal places.)

Would you be surprised to find a typist in this population whose speed exceeded 119 wpm? (Round your numerical value to four decimal places.)

It would  ---Select--- (be, not be) surprising to find a typist in this population whose speed exceeded 119 wpm because this probability is ________ , which is  ---Select--- (very small, very large) .

Suppose that two typists are independently selected. What is the probability that both their typing speeds exceed 102 wpm? (Round your answer to three decimal places.)

Suppose that special training is to be made available to the slowest 20% of the typists. What typing speeds would qualify individuals for this training? (Round your answer to the nearest whole number.)

People with typing speeds of  wpm and  ---Select--- (above, below) would qualify for the training.

What are ways to decrease sampling error?

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x', for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Table

Copy Data

Step 1 of 6:

Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6:

Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6:

Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

Step 4 of 6:

Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ.

Step 5 of 6:

Find the estimated value of y when x=42. Round your answer to three decimal places.

Step 6 of 6:

Find the value of the coefficient of determination. Round your answer to three decimal places.

Consider the following table summarizing the speed limit of a certain road and the number of accidents occurring on that road in January. Posted Speed Limit 52 50 43 36 21 22. Reported Number of Accidents 27 26 23 18 18 11. 1) Find the slope of the regression line predicting the number of accidents from the posted speed limit.Round to 3 decimal places. 2) Find the intercept of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places. 3) Predict the number of reported accidents for a posted speed limit of 25mph. Round to the nearest whole number.

Make a Frequency Distribution Chart for the following set of Data 50, 10, 25, 20, 20, 20, 50,100, 30, 15