Listed below are amounts of strontium-90 (in millibecquerels or mBq per gram of calclum) in a simple random sample of baby teth obtained from resident of state A and state B.

The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants” (Water Research, 1984: 1169-1174) suggests the uniform distribution on the interval (7.5, 20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. a. What are the mean and variance of depth? b. What is the cdf of depth? c. What is the probability that observed depth is at most 10? Between 10 and 15? d. What is the probability that the observed depth is within 1 standard deviation of the mean value? Within 2 standard deviations?

A parks and recreation department is constructing a new bike path. The path will be parallel to the railroad tracks shown and pass through the parking area al the point ${\displaystyle (4,5).}$ Write an equation that represents the path.

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. ${\displaystyle (1,3),(2,6),(3,12),(4,24)}$
Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.
Part B: Use a recursive formula to determine the time she will complete station 5.
Part C: Use an explicit formula to find the time she will complete the 9th station.

A weather forecaster predicts that the temperature in Antarctica will decrease ${\displaystyle 8^{\circ }F}$ each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least ${\displaystyle {36}^{\circ }F}$

Would you rather spend more federal taxes on art? Of a random sample of $n_1=86$ politically conservative voters, $r_1=18$ responded yes. Another random sample of $n_2=85$ politically moderate voters showed that $r_2=21$ responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use $\alpha =0.05.$

a) State the null and alternate hypotheses.

 

$H_0:p_1=p_2,H_1:p_1>p_2$

$H_0:p_1=p_2,H_1:p_1<p_2$

$H_0:p_1=p_2,H_1:p_1\ne p_2$

$H_0:p_1<p_2,H_1:p_1=p_2$

b) What sampling distribution will you use? What assumptions are you making? The Student's t. The number of trials is sufficiently large. The standard normal. The number of trials is sufficiently large.The standard normal. We assume the population distributions are approximately normal. The Student's t. We assume the population distributions are approximately normal.

c)What is the value of the sample test statistic? (Test the difference $p_1-p_2$. Do not use rounded values. Round your final answer to two decimal places.)

d) Find (or estimate) the P-value. (Round your answer to four decimal places.)

e) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level alpha? At the $\alpha =0.05$ level, we reject the null hypothesis and conclude the data are statistically significant. At the $\alpha =0.05$ level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the $\alpha =0.05$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the $\alpha =0.05$ level, we reject the null hypothesis and conclude the data are not statistically significant.

f) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters. Fail to reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters. Fail to reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters. Reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters.

Kindly answer items 1, 2, 3 and 4. Please choose the correct option.
1.The total area under the standard normal curve is__.
A-1 B.O C.0.5 D.1
2. What is the shape of a Normal Probability Distributions?
A.bar B.bell C.circle D.line
3.Which part of a normal curve is extended indefinitely both directions along thehorizontal axis, approaching but never touching it?
A.center B.tail C.top D.spread
4.Which of the following rule states that almost all data fall within the 1, 2 and 3 of standard deviation of mean when the population is normally distributed?
A. Empirical rule B. Pascal's triangle rule C. Lottery rule D. Sampling rule

An experiment designed to study the relationship between hypertension and cigarette smoking yielded the following data.
$\begin{array}{|cccc|}\hline Tensionlevel& Non-smoker& Moderatesmoker& Heavysmoker\\ Hypertension& 20& 38& 28\\ Nohypertension& 50& 27& 18\\ \hline\end{array}$
Test the hypothesis that whether or not an individual has hypertension is independent of how much that person smokes.