To explain:The purpose of the study.

For a test of Ho: p = 0.5, the z test statistic equals -1.74. Find the p-value for Ha: p < 0.5.
a. 0.0892
b. 0.0446
c. 0.0409
d. 0.9554
e. 0.0818

What is the formula to calculate the standard deviation of a sample?

90% Confidence Interval for Difference Between Two Proportions
In random, independent samples of 225 adults and 250 teenagers who watched a certain television show, 99 adults and 125 teens indicated that they liked the show. Let ${\displaystyle p_1}$ be the proportion of all adults watching the show who liked it, and let ${\displaystyle p_2}$ be the proportion of all teens watching the show who liked it. Find a 90% confidence interval for ${\displaystyle p_1-p_2}$.
1. what is the lower limit of the 90% confidence interval
2. what is the upper limit of the 90% confidence interval

Consider the region below ​$f(x)=(6-x),$above the​ x-axis, and between
$x=0andx=6.$
Let $x_i$ be the midpoint of the i th subinterval.
Approximate the area of the region using six rectangles. Use the midpoints of each subinterval for the heights of the rectangles. The area is approximately how many square units?

How would actuarial science refer to the idea that the premium should increase as number of insured entities decreases.
In other words, what is the technical term for the intuition that I would charge a higher premium per car to insure just one car than to insure 1000 cars, if such intuition is even justified.
As a sketch of my thinking on this, I have defined risk-adjusted premium as the total premium to cover losses divided by the standard deviation of the total loss on the portfolio of policies. I believe both the numerator and the denominator can be deduced from the law of large numbers.

How do ripples form and why do they spread out?
When I throw a rock in the water, why does only a small circular ring around the rock rises instead of the whole water body, and why does it fall outwards and not inwards or why fall out in any direction instead of just going back down like ball which after getting thrown up falls back to its initial position?

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.