Practice Math Statistics Problems and Master the Concepts

What is the difference between a chi square test of independence and a chi square test for homogeneity?

Aidyn Crosby 2022-10-02

At a football game, a researcher randomly asks 100 people to name their favorite sport. Is this a biased sample?

garnirativ8 2022-10-02

While including a data table for a lab report, the guidelines asked to include an uncertainty value for each raw data. In this particular lab where we used slotted masses the masses were already given (such as 50g, 200g, etc.). So while recording the masses into the data table, to how many significant figures should I record the uncertainty and for what reason?

samuelaplc 2022-10-02

Conclusion for confidence interval
If I got, let's say, a 95 % confidence interval for the mean and a 95 % confidence interval for the variance.
Would it then be wrong to conclude:
The 95 % confidence interval for the mean contains with at least 95 % probability the true mean?
and
The 95 % confidence interval for the variance contains with at least 95 % probability the true variance?
What would be a more correct/precise way to express what the confidence intervals stand for?

fofopausiomiava 2022-10-02

Classify the following random variables as continuous or discrete: the height of a sky-scraper.

Haiden Meyer 2022-10-02

Let $Z_{1}$ and $Z_{2}$ be independent standard normal random variables and $U_{1} = Z_{1}$ and $U_{2} = Z_{1} + Z_{2}$ . Are $U_{1}$ and $U_{2}$ independent? Why?

Sonia Rowland 2022-10-01

Defining confidence intervals
I have a set of n observations O. I want to calculate the mean of these observations and their confidence interval. I can do this when the observations are iid, by looking up the t-table for the required confidence value and then calculate the interval as --
$2 t \frac{σ}{\sqrt{n}}$
However, if the $i^{t h}$ observation of this sequence is related to $(i - 1)^{t h}$ observation, how do I now define the confidence interval. I believe the iid assumptions are no longer valid.

Aryan Lowery 2022-10-01

Statistics, confidence interval
I have a sample of $x_{i}$ where $x_{i} = ξ + η$ , $ξ \sim N (0, σ^{2})$ and $η \sim N (a, 1)$ i.i.d. So I need to construct confidence interval with confidence level $γ$ for $σ^{2}$ with unknown a. My attempt is, I used the following statistic: $S^{2} = \frac{\sum (x_{i} - \bar{x})^{2}}{n - 1}$ but I get an interval which could be with negative endpoints.

Sara Elsayed2022-09-30

Suppose your top drawer contains different colored socks: 6 are white, 4 are black, 16 are pink, and 12 are blue. All socks in the drawer are loose (unpaired). In the morning, you randomly select two socks, one at a time. Calculate the following probabilities, writing your answer either as a decimal or a fraction.

Litzy Downs 2022-09-30

can you write out this formula in the form of a sentence ?
$E S = \frac{\bar{X_{1}} - \bar{X_{2}}}{s}$

ivybeibeidn 2022-09-30

Assuming that these wages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
16, 35, 13, 25, 36

clovnerie0q 2022-09-30

How can I show that PGL(2,9) is not isomorphic to $S_{6}$ ?
My primary idea is to compare the size of conjugacy classes of two well-chosen elements in these groups. Is there another simpler approach?

Tia English 2022-09-30

How do you find the exact value of $\cos (\frac{π}{4} + \frac{π}{3})$ ?

Litzy Downs 2022-09-30

How do you use the angle sum identity to find the exact value of $\cos 105$ ?

Ratuiszt 2022-09-30

In order to test the difference in populations means, samples were collected for two independent populations where the variances are assumed unknown and equal and the population normally distributed. The following data resulted:
Sample 1 -
$x_{1} = 112, s_{1} = 14, n_{1} = 25$
Sample 2 -
$x_{2} = 107, s_{2} = 17, n_{2} = 28$

The value of the pooled standard deviation is approximately 15.66. True or False?

Ratuiszt 2022-09-30

How do you find the pooled standard deviation in an ANOVA table?

Dana Russo 2022-09-29

Use the applet Gamma Probabilities and Quantiles to find the medians of gamma distributed random variables with parameters In all of these cases, the median exceeds the mean. How is that reflected in the shapes of the corresponding densities?

gsragator9 2022-09-29

For each of the following situations, would you expect the random variables X and Y to be independent? Explain your answers. X is the amount of rainfall today, and Y is the rainfall at the same location tomorrow.

Isaac Barry 2022-09-29

The confidence interval is [2.663;2.937]?
The concentration of calcium in the blood for a given population follows a normal law of mean $μ = 2.8$ mmol / L and standard deviation $σ = 0.7$ mmol / L. If we take a sample of 100 people, what is the confidence interval of the calcium concentration at the 95% confidence level.
I got the confidence interval [2.663; 2.937] but I think this is wrong.

Kelton Bailey 2022-09-29

What is the difference between confidence interval and the width of confidence interval?
Let $X_{1}, . . ., X_{n}$ be n random samples of a normal distribution $X \sim N (μ, 4)$ where $μ$ is unknown. Write down the 95% confidence interval of $μ$ in terms of n. What sample size n is required such that the width of this confidence interval is barely larger that 0.5?

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