Statistics Projects for High School Students

For healthy adults, the mean pH level is ${\displaystyle \mu =7.4}$, a new drug for arthritis has been developed. However, it is throught that this drug may change blood pH. A random sample of 33 patients with arthritis took the drug for three months. Blood tests showed that the sample mean from these 33 patients was a pH of 8.0 and it is known that ${\displaystyle \sigma =2.3}$. (Note, there is no unit for this type of data). Use ${\displaystyle \alpha =0.05}$ level of significance to test the claim that the drug has increased the mean pH level of the blood.
If we use the classical approach, what would the criterion (step 3) be?
1) -1.645 or less
2) -2.33 or less
3) 1.645 or more
4) 2.33 or more

Suppose that there are n kids numbered 1,2,...,n. You have m candies, you are distributing the candies to the kids using the following experiment: For each candy uniforn at random pick a kid an give the candy to her. A kid is unlucky, if she does not get any candy. Use union bound to derive an upper bound on the probability that there is at least one unlucky kid.

Data was collected for 259 randomly selected 10 minute intervals. For each ten-minute interval, the number of people entering the atrium of a large mall were recorded. The data is summarized in the table below.
$$\begin{array}{|cc|}\hline \text{Number of Guests}& Frequency\\ 100-119& 57\\ 120-139& 65\\ 140-159& 38\\ 160-179& 15\\ 180-199& 84\\ \hline\end{array}$$
What is the class width for this GFDT?
Class width = ?

$$\begin{array}{|c|}\hline \text{Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation}y=mx+by=mx+b\\ x123456\\ y7795123134159184\\ \hline\end{array}$$

Deviation boundary% of data points within boundary Probability of any particular data point being outside boundary +20 +36 68.0 95.40 99.70 Csp Tm 8.00M dCi 32.0% 4.60% 0.30%

Construct the cumulative frequency distribution for the given data.
$$\begin{array}{|cc|}\hline \text{Age (years) of Best Actre when award was won}& Frequency\\ 20-29& 29\\ 30-39& 33\\ 40-49& 14\\ 50-59& 2\\ 60-69& 5\\ 70-79& 1\\ 80-89& 1\\ \hline\end{array}$$
$$\begin{array}{|cc|}\hline \text{Age (years) of Best Actre when award was won}& \text{Cumulative Frequency}\\ \text{Less than 30}& ?\\ \text{Less than 40}& ?\\ \text{Less than 50}& ?\\ \text{Less than 60}& ?\\ \text{Less than 70}& ?\\ \text{Less than 80}& ?\\ \text{Less than 90}& ?\\ \hline\end{array}$$

Kelly flips a coin 20 times. The results are shown in the table, where "H" represents the coin landing heads up and "T" represents the coin landing tails up.
$$\begin{array}{|cccccc|}\hline Flip& 1& 2& 3& 4& 5\\ Result& H& T& T& H& H\\ \hline\end{array}$$
$$\begin{array}{|cccccc|}\hline Flip& 6& 7& 8& 9& 10\\ Result& H& H& T& H& T\\ \hline\end{array}$$
$$\begin{array}{|cccccc|}\hline Flip& 11& 12& 13& 14& 15\\ Result& H& T& T& T& H\\ \hline\end{array}$$
$$\begin{array}{|cccccc|}\hline Flip& 16& 17& 18& 19& 20\\ Result& T& H& H& T& H\\ \hline\end{array}$$
1) The theoretical probability that the coin will land heads up is ?
2) Based on the data, the experimental probability that the coin will land heads up is ?
3) The experimental probability is ? than the theoretical probability.

Monitor three consecutive packets going through an internet router. Based on the packet header, each packet can be classified as either video (v) if it was sent from a YouTube server or as ordinary data (d). For example, two video packets followed by one data packet corresponds to vvd. Assume that v and data packets are equally likely, and they occur in an independent manner.
a) Calculate probability of observing the packets: vvd
b) Calculate the probability of observing 4v packets in 8 packets.

A coach collected data for the same group of runners for two weeks. The median distance run for Week 1 was 14.5 miles, with an IQR of 1.15. The median distance run for Week 2 was 16 miles, with an IQR of 1.5.
Write a word or phrase from the box on the bla
to correctly compare the variability of data from Week 1 to Week 2.
mean IQR closer to farther from
The Week 2 data values tend to be 5 their median than the Week 1 data values are to their median because Week 2 has a greater 6.

Given the data, find the relative frequency between 12-15
$$\begin{array}{|cc|}\hline Grade& Frequency\\ 0-3& 3\\ 4-7& 7\\ 8-11& 9\\ 12-15& 6\\ 16-19& 5\\ \hline\end{array}$$
a. 20%
b. 23%
c. None of these
d. 20%
e. 10%

Uniform distribution is defined over the interval from 2 to 5.
What is the standard deviation?

The mean number of birth of babies over a 7 month period in lbri is 106 and the coefficient of variation of the data is 5.21%. Find the standard deviation of the data.
1) 5.5226
2) 7.0226
3) 4.5226
4) 6.5226

Based on an analysis of sample data, an article proposed the pdf ${\displaystyle f\left(x\right)=0.65e^{-0.65(x-1)}}$ when ${\displaystyle x\ge 1}$ as a model for the distribution of ${\displaystyle X=}$ time (sec) spent at the median line.
(a) What is the probability that waiting time is at most 4 sec? More than 4 sec?
at most 4 sec ${\displaystyle P(X\le 4)=?}$
more than 4 sec ${\displaystyle P\left(X>4\right)=?}$
(b) What is the probability that waiting time is between 3 and 7 sec?

If the Bit Error Rate (BER) in a wireless communication system in 0.5%, then find the following at the receiving side,
A. How many errors (in bits) will be there if a 100MB file is sent?
B. What is the probability of exactly 6 errors (in bits) if a 100MB data is sent?
C. What is the probability of 4 or less than 4 errors (in bits) if a 100MB data is sent?

Suppose that the number of car accidents per day in Wilmington, NC has been recorded for the past year. The table below is a probability distribution table representing the data collected.
$$\overline{)\begin{array}{cccccc}\text{Number of accidnets}& 0& 1& 2& 3& 4\\ Probability& & .12& .32& .25& .13\end{array}}$$
b) Find the probability that there will be at least 2 accidents

From a classroom of 26 students, the number of students taking Data Management is 13, the number taking Calculus is 9. There are 5 students who are not taking either course.
How many students are taking both Calculus and Data Management?

Directions: Find ${\displaystyle P_{11}{P}_7,\text{and}{P}_{88}}$ of the given set of ungrouped data.
33,30,32,44,35,38,37,26,31,34,44,39,25,41,37,21,22,15,42, 25

A certain data set has a variance of 9. Find the standard deviation of the data set.

Kelly performs a hypothesis test and calculates a p-value of .03 for her sample data. What decision can be made about the null hypothesis?
1) fail to reject the null
2) reject the null