Practice Math Statistics Problems and Master the Concepts

The times that a cashier spends processing each person’s transaction are independent and identically distributed random variables with a mean of µ and a variance of $σ^{2}$ . Thus, if Xi is the processing time for each transaction, $E (X_{i}) = μ$ and $Var (X_{i}) = σ^{2}$ . Let Y be the total processing time for 100 orders: $Y = X_{1} + X_{2} + \dots + X_{100}$
a) What is the approximate probability distribution of Y, the total processing time of 100 orders?
b) Suppose for $Z \sim N (0, 1)$ , a standard normal random variable: $P (a < Z < b) = 100 (1 - α) %$ . Using your distribution from part (a), show that an approximate $100 (1 - α) %$ confidence interval for the unknown population mean $μ$ is: $(\frac{Y - 10 b σ}{100}) < μ < (\frac{Y - 10 a σ}{100})$
I have done part (a) and ended up with $Y \sim N (100 μ, σ^{2})$ using the central limit theorem, but I am unsure of where to start in part (b).

Dylan Yoder 2022-04-09

The results of a significance test for the difference of two proportions would be the same as a chi-squared test for independence for two variables with two levels.
Group of answer choices:
-True
-False
If one of the categorical variables has 3 or more levels then we can consider the difference of proportions and use the normal distribution to determine the p-value.
Group of answer choices:
-True
-False
If the results of the chi-squared test for independence turn out to be significant then we can guarantee the variables are dependent.
Group of answer choices:
-True
-False

amara labonog2022-04-09

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 121.1-cm and a standard deviation of 2.2-cm. For shipment, 26 steel rods are bundled together.

Find P91, which is the average length separating the smallest 91% bundles from the largest 9% bundles.
P91 = -cm

Enter your answer as a number accurate to 2 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

A population of values has a normal distribution with $μ = 121.3$ and $σ = 5.8$ . You intend to draw a random sample of size $n = 149$ .
Find the probability that a single randomly selected value is between 119.8 and 121.2.
P(119.8 < X < 121.2)
Find the probability that a sample of size $n = 149$ is randomly selected with a mean between 119.8 and 121.2.
P(119.8 < M < 121.2)
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Izabelle Walsh 2022-04-08

For a goodness-of-fit test with $α = 0.10$ and 5 categories, what is the critical χ2 value?

alahovom7ahc 2022-04-08

Finding upper confidence limit without mean and sd
So the question I'm trying to answer looks like this:
We are interested in p, the population proportion of all people who are currently happy with their cell phone plans. In a small study done in 2012, it was found that in a sample of 150 people, there were 90 who were happy with their cell phone plans.
Find the upper confidence limit of an 82% confidence interval for p.
I know the formula is $estimate \pm (criticalvalue) (standard error)$

Justine White 2022-04-08

Identify a correct test to use to test the claim (some claims may be tested using more than one test). Assume al assumptions for the tests are met. Tests may be used more than once or not at all.
a. One sample t-test
b. Two sample t-test
c. Matched pairs test
d. One sample proportion z-test
e. Two sample proportion z-test
f. Slope t-test for linear regression
g. ANOVA test for linear regression
h. One-way ANOVA
i. Chi-square test for independence
j. Chi-square test for goodness of fit
A. The distribution of Starburst colors is 25% red, 25% orange, 25% pink, and 25% yellow.
B. Gas costs more, per gallon, at Shell stations than at Mobil stations across the street from them
C. There is no relationship between how much you eat (in calories) and your weight.
D. When people experience pain, they report less pain when they swear than when they don't swear.
E. One-third of American adults can't identify the United States on a world map.
F. Men are more likely to drive and text than women are.
G. Undergraduates in every CSUF College, on average, have the same GPA
H. On average, a "gallon of milk" contains less than 1 gallon.
I. Knowing your favorite burger chain tells me nothing about whether you prefer pancakes or waffles.
J. The more money you have, on average, the more problems you have.

painter555ui8n 2022-04-08

How to get the population standard deviation from a sample standard deviatoin
I am trying to find the confidence interval, and I need to know the population standard deviation. If I am given the sample standard deviation, how can I get the population one? Thanks!

Kendal Day 2022-04-08

Trouble Understanding the Formal Definition of a Confidence Interval
A $1 - α$ confidence interval for a paramater $θ$ is an interval $C_{n} = (a, b)$ where $a = a (X_{1}, \dots, X_{n})$ and $b = b (X_{1}, \dots, X_{n})$ are functions of the data such that
$P_{θ} (θ \in C_{n}) > 1 - α, for all θ \in Θ$
If $θ$ is a vector then we use a confidence set (such as a sphere or an ellipse) instead of an interval.
Question:
While I understand conceptually what a confidence interval is (i.e., a 95% CI means that 95% of experiments will trap the paramater in the interval), I don't understand how this formality is capturing this concept.
In particular, I don't understand what is meant by the notion of $P_{θ} (θ \in C_{n})$ . What is the sample space which P is drawing from? What is the set $θ \in C_{n}$ ? It seems here $θ$ is being treated both as a fixed value (from the notation Pθ) and as a random variable (by the notation $θ \in C_{n}$ ).

Darian Silva 2022-04-07

For each of the following examples, state whether the chi-square goodness-of-fit or the chi-square test for independence is appropriate.
15a. An instructor tests whether class attendance (low, high) and grade point average (low, average, high) are independent.
A. goodness of fit test
B. test for independence
15b. An educator tests whether the teacher's speaking style (monotone, dynamic) and student interest (low, high) are independent.
A. goodness of fit test
B. test for independence
15c. A sports psychologist compares the number of athletes with Type A or Type B personality traits.
A. goodness of fit test
B. test for independence
Any help

Alessandra Carrillo 2022-04-07

For fixed k, the variables $(2 k + 1) {\hat{f}}_{k} (λ)$ are asymptotically distributed according the Gamma distribution with shape parameter $2 k + 1$ and mean $(2 k + 1) f_{X} (λ)$ . It turns out that this suggests a confidence interval of the form
$(\frac{(4 k + 2) {\hat{f}}_{k} (λ)}{χ_{{4 k + 2, 1 - α}}^{2}}, \frac{(4 k + 2) {\hat{f}}_{k} (λ)}{χ_{{4 k + 2, α}}^{2}})$
where $χ_{{k, α}}^{2}$ the $α$ -quantile of the chi-square distribution with k degrees of freedom.
To show that this interval is asymptotically of level $1 - 2 α$

Adison Palmer 2022-04-07

Fingerprint analysis and blood grouping are features that do not change through the lifetime of an individual. Fingerprint features appear early in the development of a fetus, and blood types are determined by genetics. Therefore, each is considered an effective tool for identification of individuals. These characteristics are also of interest in the discipline of biological anthropology—a scientific discipline concerned with the biological and behavioral aspects of human beings.
(a) Is the test for an association in this case a chi-square test of independence, or a chi-square test of homogeneity? Justify your choice.
(b) Identify the conditions for the chi-square inference procedure selected in part (a), and indicate whether the conditions are met.
(c) The resulting chi-square test statistic from the appropriate test is approximately 18.930. What are the degrees of freedom and p-value of the test?
(d) Biological anthropology is concerned with the comparative study of human origin, evolution and diversity. Considering the sampling design in this study, to what population is it reasonable for the researchers to generalize their results?
$\begin{array}{cc} Blood Type \\ A & B & A B & O & Total \\ Loops & 66 (71.69) & 99 (112.19) & 35 (32.29) & 101 (84.83) & 301 \\ Whorls & 51 (47.16) & 91 (73.80) & 15 (21.24) & 41 (55.80) & 198 \\ Arches & 14 (12.15) & 15 (19.01) & 9 (5.47) & 13 (14.37) & 51 \\ Total & 131 & 205 & 59 & 155 & 550 \end{array}$

In a family of 6, what is the probability of getting 1 boy and 5 girls

Justine Webster 2022-04-07

Are there any theoretical considerations between p-value and the Bayesian statistics? I mean say, any theorem regarding both of these two concepts at a time.

Marco Villanueva 2022-04-07

Risk analysis is an important part of holistic risk management. What is risk analysis and why is it important? How do organizations conduct risk analysis? How is qualitative risk analysis different than quantitative risk analysis? In what ways does traditional accident analysis help an organization conduct risk analysis? How does root cause analysis enhance the results of traditional risk analysis?

Jayla Faulkner 2022-04-07

A pregnancy test kit is 98.5% accurate for true positive result, i.e. the result is positive when the tester is actually pregnant. If she is not pregnant, however, it may yield a 0.8% false positive. Suppose a woman using this pregnancy kit is 60% at risk of being pregnant.
Not sure about her first test which turned out to be negative, the woman decides to take the test again. This second test, however, turns out to be positive. Assuming the two test are independent, find the probability that she is actually pregnant.
Now she is so confused whether or not she is pregnant. So she take the tests n more times and the results for these n more tests are all positive. Find the minimum value for n so that she can be at least 99.99% sure of pregnancy, assuming all test are independent.

Logan Lamb 2022-04-07

__________ involves prioritizing risks based on their probability and impact ofoccurrence.
Qualitative risk analysis
Risk response planning
Quantitative risk analysis
Risk management planning

Ashley Fritz 2022-04-07

Why does the flame of a gas stove not spread backwards?
On lighting a gas stove the flame is active only above the burner. However, the gas input from beneath the burner and all the way to the pipeline contains gas fuel. Why doesn't it all ignite up ? I am guessing it may be due to the pressurised flow of the fuel in one direction but then I am unable to relate it to combustion, i.e., if a combustible substance is in contact of a source of ignition then it should start to burn.

kazue72949lard 2022-04-07

When the Bureau of Labor Statistics conducts a survey, it begins by partitioning the United States adult popula- tion into 2,007 groups called primary sampling units Assume that these primary sampling units all contain the same number of adults. If you randomly select one adult from each primary sampling unit, is the result a simple random sample? Why or why not?

Daphne Haney 2022-04-07

The prevalence of breast cancer in women over 40 in country X is estimated to be 0.8% (i.e., 8 in every 1,000 women in that age group).
Mammograms test for the presence of breast cancer. A positive result indicates that the disease is present. A negative result indicates that it is not.
The sensitivity of a mammogram test for breast cancer is estimated to be 90%. This is the probability that the mammogram will give a positive result when the person being tested does have breast cancer.
The false positive rate for the mammogram is 7.5%. This is the probability that the mammogram will give a positive test result when the person being tested does not have breast cancer.
All women who test positive (816) in the mammogram are referred for a further, different examination, which however has the same sensitivity and false positive rates as the first test.
What is the probability that a woman referred for this examination and testing positive again, actually does have breast cancer?

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