Improve Your Understanding of College Level Statistics Problems

The lengths of the products produced in a production process are controlled. The standard deviation is 0.45 mm. A quality control specialist keeps checking over 40 units randomly every morning. Average length in one day 35.62mm. when it happens. Which of the following is the confidence interval for the mean population mean at ${\displaystyle 95\mathrm{\%}}$ confidence level?
A) ${\displaystyle P\left(60<\mu <70\right)=0,95}$
B) ${\displaystyle P\left(30<\mu <40\right)=0,05}$
C) ${\displaystyle P\left(30<\mu <40\right)=0,95}$
D) ${\displaystyle P\left(60<\mu <70\right)=0,05}$
E) ${\displaystyle P\left(70<\mu <80\right)=0,95}$

Use the Student's t distribution to find $t_c$ for a 0.95 confidence level when the sample is 24. (Round your answer to three decimal places.)

How do you solve?
A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data for a particular clinics follows (the reported variable is the number of CAT scans each month expressed as the number of CAT scans per thousand members of the health plan):
2.31,2.09,2.36,1.95,1.98,2.25,2.16,2.07,1.88,1.94,1.97,2.02.
Find a two-sided ${\displaystyle 95\mathrm{\%}}$ confidence interval for the standard deviation. What should you do to address any reservations about this confidence interval?
Round your answers to two decimal places (e.g. 98.76).
$\le \sigma \le$

Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below.
a. Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence intervals limits accordingly.
${\displaystyle 13.05Mbps<\mu <22.15}$ Mbps
b. Identify the best point estimate of ${\displaystyle \mu }$ and the margin of error.
The point estimate of ${\displaystyle \mu }$ is 17.60 Mbps.
The margin of error is ${\displaystyle E=?}$ Mbps.

A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts of mercury​ (ppm) found in tuna sushi sampled at different stores in a major city. Construct a ${\displaystyle 95\mathrm{\%}}$ confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna​ sushi?
$\begin{array}{|ccccccc|}\hline 0.60& 0.82& 0.09& 0.89& 1.29& 0.49& 0.82\\ \hline\end{array}$
What is the confidence interval estimate of the population mean ${\displaystyle \mu ?}$
${\displaystyle ?p\pm <\mu <?p\pm }$

A privately owned liquor store operates both a drive-n facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-in and walk-in facilities are in use, and suppose that the joint density function of these variables is
$f(x,y)=\{\begin{array}{ll}\frac{2}{3}(x+2y)& 0\le x\le 1,0\le y\le 1\\ 0& ,elsewhere\end{array}$
a) Find the marginal density of X.
b) Find the marginal density of Y.
c) Find the probability that the drive-in facility is busy less than one-half of the time.

The monthly incomes for 12 randomly selected​ people, each with a​ bachelor's degree in​ economics, are shown on the right. Complete parts​ (a) through​ (c) below.
Assume the population is normally distributed.
a) Find the sample mean.
b) Find the sample standard deviation
c) Construct a ${\displaystyle 95\mathrm{\%}}$ confidence interval for the population mean ${\displaystyle \mu }$. A ${\displaystyle 95\mathrm{\%}}$ confidence interval for the population mean is
$\begin{array}{|ccc|}\hline 4450.42& 4596.96& 4366.46\\ 4455.62& 4151.52& 3727.77\\ 4283.26& 4527.94& 4407.68\\ 3946.49& 4023.61& 4221.73\\ \hline\end{array}$

Two different analytical tests can be used to determine the impurity level in steel alloys. Nine specimens are tested using both procedures, and the results are shown in the following tabulation.
$\begin{array}{|ccc|}\hline Specimen& Test-1& Test-2\\ 1& 1.2& 1.4\\ 2& 1.6& 1.7\\ 3& 1.5& 1.5\\ 4& 1.4& 1.3\\ 5& 1.8& 2.0\\ 6& 1.8& 2.1\\ 7& 1.4& 1.7\\ 8& 1.5& 1.6\\ 9& 1.4& 1.5\\ \hline\end{array}$
Find the ${\displaystyle 95\mathrm{\%}}$ confidence interval for the mean difference of the tests, and explain it.

Express the confidence interval $57.7\mathrm{\%}\pm 4.9\mathrm{\%}$ in interval form.
Express the answer in decimal format (donot eter as percents).

Anystate Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was $1570. Assume $\sigma math=\$250$. Find 0.90 and 0.99 confidence intervals for the mean claim payment.

Using the daily high and low temperature readings at Chicago's O'Hare International Airport for an entire year, a meteorologist made a scatterplot relating y = high temperature to x = low temperature, both in degrees Fahrenheit.

After verifying that the conditions for the regression model were met, the meteorologist calculated the equation of the population regression line to be  $[{\mu }_y=16.6+1.02]with[\sigma =6.6{+}^{\circ }F]$

If the meteorologist used a random sample of 10 days to calculate the regression line instead of using all the days in the year, would the slope of the sample regression line be exactly 1.02? Explain your answer.