Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in mineral content of the spines of 47 mothers during three months of breast-feeding. The sample mean is -3.587%. Let us assume that these 47 women as an SRS from the population of all nursing mothers. Suppose that the percent change in this population has standard deviation 2.5%.

The hypothesized value μ0=−2.7% falls inside this confidence interval. Carry out the z-test for H0:μ=−2.7% against the two-sided alternative. Show that the test is not significant at the 1% level.

A population has a mean of 128 and a standard deviation of 32. Suppose a sample of size 64 is selected and x is used to estimate μ. (Round your answers to four decimal places.)

(a) What is the probability that the sample mean will be within ±5 of the population mean?

(b) What is the probability that the sample mean will be within ±10 of the population mean?

You may need to use the appropriate appendix table or technology to answer this question.

A simple random sample of 60 items resulted in a sample mean of 70. The population standard deviation is

σ = 5.

(a)

Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)

to

(b)

Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.)

to

(c)

What is the effect of a larger sample size on the interval estimate?

A larger sample size provides a larger margin of error.A larger sample size provides a smaller margin of error.    A larger sample size does not change the margin of error.

Samples of peanut butter produced by three different manufactures are tested for aflatoxin (ppb), with the following results:

Use the 0.05 level of significance to test whether the differences among the 3 sample means are significant.

At a train station, international trains arrive at a rate λ = 1. At the same train station national trains arrive at rate λ = 2. The two trains are independent.

What is the probability that the first international train arrives before the third national train?

Select one (1) project from your working or educational environment that you would use the hypothesis test technique. Next, propose the hypothesis structure (e.g., the null hypothesis, data collection process, confidence interval, test statistics, reject or not reject the decision, etc.) for the business process of the selected project. Provide a rationale for your response. Evaluation

You are the production manager for a part manufacturing company. There are 2 manufacturing locations, plant A and B. you suspect there is a difference in the proportion of rejected parts that are manufactured at Plant A as compared to plant B. for a week you observed:

The proportion of rejected parts was 200/4000=5%. If there were no difference between the proportion of rejected parts whether there were manufactured at either plant A or plant B then you would estimate:

You decide to preform a chi squared test to determine if there is statistically a difference between the proportion of rejected parts manufactured at plant A as compared to the proportion of rejected parts manufactured at plant B.

1. State your null and alternate hypothesis. B) at the 5% level of significance, is there evidence of a difference between the proportions of rejected parts manufactured at plant A as compared to plant B? based on your hypothesis test what is your conclusion? State your conclusion formally.

1. Determine the value for the constant "k" that will make the function below a PDF.

f(x) = k x^4 for x in (0,2) and f(x) = 0, for all other x ; k =

A. 8/3 B. 3/8 C. 3/64 D. 22/7 E. None of these

2. In a dice tossing random experiment , a red die and a green die are thrown independently . Consider as a random variable, X, the range in showing dots. for example if the red die is 6 and the green die is 4 , then the random variable has a value of 2 in that experiment. Calculate the probability, Pr(x=1) =

A) .278 B) .167 C) .111 D) .0556

3. Assume Z is a standard normal random variable, what is the area to right of z = -1.23

A) .1093 B) .8907 C) .3594 D) .6406 E) None of these  

The College Board National Office recently reported that in 2011–2012, the 547,038 high school juniors who took the ACT achieved a mean score of 515 with a standard deviation of 129 on the mathematics portion of the test (http://media.collegeboard.com/digitalServices/pdf/research/2013/TotalGroup-2013.pdf). Assume these test scores are normally distributed.

1. What is the probability that a high school junior who takes the test will score at least 590 on the mathematics portion of the test? If required, round your answer to four decimal places.
   
   P (x ≥ 590) =
   
2. What is the probability that a high school junior who takes the test will score no higher than 510 on the mathematics portion of the test? If required, round your answer to four decimal places.
   
   P (x ≤ 510) =
   
3. What is the probability that a high school junior who takes the test will score between 510 and 590 on the mathematics portion of the test? If required, round your answer to four decimal places.
   
   P (510 ≤ x ≤ 590) =
   
4. How high does a student have to score to be in the top 10% of high school juniors on the mathematics portion of the test? If required, round your answer to the nearest whole number.
   

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.7 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer.

1. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. If required, round your answers to four decimal places.
   

   	Lq	=
   	L	=
   	Wq	=  hours
   	W	=  hours
   	Pw	=

2. Service goals dictate that an arriving customer should not wait for service more than an average of 6 minutes. Is this goal being met? If not, what action do you recommend?
   
   
   
3. If the consultant can reduce the average time spent per customer to 9 minutes, what is the mean service rate? If required, round your answer to one decimal place.
   
   ??? customer per hour
   
   Will the service goal be met?
   
   

Explain how randomization, in general, can obtain balance on measured and unmeasured confounding

Describe one probability sampling strategy and one nonprobability sampling strategy.

A dietary supplement is promising weight loss in 2 weeks using their product. A sample of 10 people were weighed before starting the supplement and 2 weeks after using the supplement. Using a 5% significance level, is there statistically sufficient evidence to support the claim that there was weight loss after taking the supplement for 2 weeks? Perform an appropriate hypothesis test showing necessary statistical evidence to support your conclusion.

CONCLUSION:

There are a number of companies that provide a delivery service for take away meals. One of the important factors for the customer is the time between placing an order and receiving the meal. A particular Thai restaurant use two different delivery companies. Company A delivers 40% of their orders while Company B delivers the rest. A survey of customers using the service have indicated they want their food delivered within 30 minutes. Historically, Company B has experienced 10% of their orders taking longer than 30 minutes to deliver while Company A has been late on 15% of their orders.

a. We will use A to represent the event ‘Company A delivers the order’ and L to represent the event ‘The meal is delivered late’. Use the correct statistical notation and words to define the complement of both A and L. (Use this terminology in your working throughout the remainder of this question).

b. Construct a fully labelled probability tree to describe this problem with the outcomes and probabilities shown along each branch.

c. A customer has just received their order. What is the probability the order was delivered on time, that is, within 30 minutes of placing the order?

d. A customer who contacted the Thai restaurant reported receiving their order 45 minutes after placing the order. Which company is most likely to have delivered the order? Use probabilities to support your conclusion.

e. Considering the probability calculated in part c., should the restaurant owner have any concerns about the reliability (delivery times) of the delivery companies they use? Explain.