Showing steps of calculation will NOT be necessary. Only answers are required. Need to show graph if the question is asked or needed. 1: The weights of packets of cookies produced by a manufacturer...


Showing steps of calculation

will NOT

be necessary. Only answers are required. Need to show graph if the question is asked or needed.


1:
The weights of packets of cookies produced by a manufacturer have a normal distribution with mean 202 grams and standard deviation 3 grams. What is the weight that should be written on the packet so that only 1 percent is underweight?

2:A company receives a very large shipment of components. A random sample of sixteen of these components is checked, and the shipment is accepted if fewer than two of the sampled components are defective. What is the probability of accepting a shipment containing 25% defectives?

3:
You are interested in the proportion of smokers. Consider a population consisting of N = 4 elements: the first two persons smoke, while the remaining two do not smoke. That is {S, S, N, N}

(a)
In this population, what is the proportion of smokers?

(b)
You take a random sample of size n = 2. How many different random samples are possible?

(c)
Write down the sampling distribution of P, the sample proportion of smokers in a random sample of size n = 2 from this population. That is, list the possible outcomes (sample proportions of smokers) and the associated probabilities.

(d)
Calculate the mean of the sampling distribution.

4:
The average fill volume from a random sample of 49 bottles of an energy drink is 32.8 ounces; the standard deviation among the individual fill volumes is 3.5 ounces. Determine a 95 percent confidence interval for the mean fill weight.

5:
Continuation of previous problem. Determine the probability value for testing the research hypothesis that the mean fill volume is less than 33 ounces. Use the sample information in the previous problem and state your conclusion assuming a significance level of 5 percent.

6:
We are interested in the proportion of UoI students who smoke. A random sample of n = 400 UoI students is taken. The proportion of smokers in this random sample is 0.25.
Calculate a 95 percent confidence interval for the unknown proportion of smokers among the UoI student population.

7:
Consider the following regression model:
Salary(in $ 1000) = 20 + (2)X + (5)Z + (0.7)(X*Z)
where X is the number of years of experience, and Z is an indicator variable that is 1 if you have obtained an MBA degree and 0 otherwise; X*Z is the product between years of experience and the indicator variable Z.
Graph salary (Y) against years of experience (X). Do this for both groups (without MBA, with MBA) on the same graph.
Does experience matter? Is it worth getting an MBA? Interpret the graph.

8:
The temperature in Jihlava follows a normal distribution with mean 50 degrees and standard deviation 10 degrees. You select one day at random. What is the probability that at that day the temperature will be above 60?

9:
A consignment of twelve electronic components contains one component that is faulty. Two components are chosen randomly from this consignment for testing. What is the probability that the faulty component will be one of the two components chosen for testing?

10:
Consider the following four scatter diagrams. The correlation coefficients for these four data sets are given by: -1, -0.6, 0.4 and 0.9. Assign the correlation coefficients to these four scatter diagrams

11:
Consider the following four data sets of 4 observations each:
Set 1: 1010, 1011, 1012, 1013
Set 2: 11, 10, 9, 8
Set 3: 5, 7, 9, 11
Set 4: 9, 10, 7, 8
Which data set has the largest standard deviation?
[No calculations needed]



12:
Below, we show the scatter plot of n = 12 observations on monthly expenses (Y) and monthly sales (X) of a small manufacturing firm. A partial computer output of the regression model, , is also given.

13 :
A set of 20 data values has a median and mean of $1425, and ranges from a minimum value of $987 to a maximum value of $1945. Later we discover that the $1945 value was mis-recorded and should have been $2945.

(a)
Find the corrected value for the
median.

(b)
Find the corrected value for the
mean.

14:
In order to prove/disprove the null hypothesis that there is no salary discrimination, you obtain random samples of male and female employees in your company. From the sample of 30 men you find an average yearly salary of $ 60,000 (standard deviation $ 4,000). From the sample of 30 women you find an average salary of $ 58,500 (standard deviation $ 5,000). Your research hypothesis is that the mean salaries for men and women are different.
Draw your conclusion at significance level 0.05.

15:
The knowledge of basic statistical concepts of 36 engineers selected at random was measured on a scale of 100, before and after a short course in statistical quality control. This resulted in the following table:


Test the research hypothesis that the course in statistical quality control improves the knowledge of statistics at the 0.05 significance level.



16:
Your job as marketing manager of a large chain is to watch the overall market situation in many districts. The results of a sample of 6 districts show that the situation has improved in 5 out of the 6 markets. Can you claim that the market situation has improved? Calculate the probability value and compare with significance level 0.05.

Hint:
The null hypothesis says that change (up or down) is equally likely (= 0.5).

17:
AnnoyCo, a large consumer products firm, has recently introduced a new product. As part of the launch, 25% of the customers in the company’s database received calls from AnnoyCo’s telemarketers.
It is now one year after the launch of the product. 40% of the customers in the company’s database have purchased the product.
A recent survey by the company’s marketing department has determined that among customers who have bought the product, one of eight were called.

(a)
What is the probability that a customer chosen at random from the company’s data base has bought the product?

(b)
What is the probability that this customer was called and bought the product?

(c)
Given that the customer was called, what is the probability he or she bought the product?

(d)
Did telemarketing help the company’s sales? Explain in a sentence or two.
May 12, 2022
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