Find the following probabilities for the standard normal random variable z:

(a) P(−0.76<z<0.75)=

(b) P(−0.98<z<1.36)=

(c) P(z<1.94)=

(d) P(z>−1.2)=

2.

Suppose the scores of students on an exam are Normally distributed with a mean of 480 and a standard deviation of 59. Then approximately 99.7% of the exam scores lie between the numbers ---- and -----. ??

Hint: You do not need to use table E for this problem.

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.4 pounds, what is the probability that the sample mean will be each of the following?

a. More than 59 pounds

b. More than 57 pounds

c. Between 56 and 57 pounds

d. Less than 53 pounds

e. Less than 48 pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

Contingency tables may be used to present data representing scales of measurement higher than the nominal scale. For example, a random sample of size 20 was selected from the graduate students who are U.S. citizens, and their grade point averages were recorded. 3.42 3.54 3.21 3.63 3.22 3.8 3.7 3.2 3.75 3.31 3.86 4 2.86 2.92 3.59 2.91 3.77 2.7 3.06 3.3 Also, a random sample of 20 students was selected from the non-U.S. citizen group of graduate students at the same university. Their grade point averages were as follows. 3.50 4.00 3.43 3.85 3.84 3.21 3.58 3.94 3.48 3.76 3.87 2.93 4.00 3.37 3.72 4.00 3.06 3.92 3.72 3.91 Test the null hypothesis that the proportion of graduate students with averages of 3.50 or higher is the same for both the U.S. citizens and the non-U.S. citizens

A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 5 doors is made, and it is found that they have a mean of 2047 millimeters with a standard deviation of 10 . Is there evidence at the 0.05 level that the doors are too short and unusable? State the null and alternative hypotheses for the above scenario.

A realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City. [You may find it useful to reference the t table.] Property Taxes Size 21892 2498 17421 2419 18170 1877 15679 1011 43962 5607 33657 2575 15300 2248 16789 1984 18108 2021 16794 1311 15113 1327 36069 3033 31058 2871 42126 3346 14392 1533 38911 4032 25323 4041 22972 2446 16160 3596 29215 2871

a-1. Calculate the sample correlation coefficient rxy. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

A political scientist is interested in the effectiveness of a political ad about a particular issue. The scientist randomly asks 18 individuals walking by to see the ad and then take a quiz on the issue. The general public that knows little to nothing about the issue, on average, scores 50 on the quiz. The individuals that saw the ad scored an average of 49.61 with a standard deviation of 5.02. What can the political scientist conclude with an α of 0.01?

a) What is the appropriate test statistic?
---Select--- na z-test one-sample t-test independent-samples t-test related-samples t-test

b)
Population:
---Select--- the political ad general public the particular issue individuals walking by the ad
Sample:
---Select--- the political ad general public the particular issue individuals walking by the ad

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

Individuals that watched the political ad scored significantly higher on the quiz than the general public.Individuals that watched the political ad scored significantly lower on the quiz than the general public.    Individuals that watched the political ad did not score significantly different on the quiz than the general public.

True or False? A hypothesis test is conducted at to test whether the population correlation coefficient is zero. If the sample size is 25 and the sample correlation coefficient is 0.6, then the critical values of the student t that define the upper and lower tail rejection areas are 2.069 and -2.069, respectively.

The developers of a new online game have determined from preliminary testing that the scores of players on the first level of the game can be modelled satisfactorily by a Normal distribution with a mean of 185 points and a standard deviation of 28 points. They would like to vary the difficulty of the second level in this game, depending on the player’s score in the first level. (a) The developers have decided to provide different versions of the second level for each of the following groups: (i) those whose score on the first level is in the lowest 25% of scores ii) those whose score on the first level is in the middle 50% of scores (iii) those whose score on the first level is in the highest 25% of scores. Use the information given above to determine the cut-off scores for these groups. (You may round each of your answers to the nearest whole number.) (b) In the second level of the game, the developers have also decided to give players an opportunity to qualify for a bonus round. Their stated aim is that players from group (i) should have 75% chance of qualifying for the bonus round, players from group (ii) should have 55% chance of qualifying for the bonus round and that players from group (iii) should have 30% chance of qualifying for this round. Let ?, ? and ? respectively denote the events that a player’s score on the first level was in the lowest 25% of scores, the middle 50% of scores and the highest 25% of scores, and let ? denote the event that the player qualifies for the bonus round. Use event notation to express the developers’ aim as a set of conditional probabilities. (c) Based on the developers’ stated aim, find the total probability that a randomly chosen player will qualify for the bonus round. (d) Given that a player has qualified for the bonus round, what is the probability that the player’s score on the first level was in the middle 50% of scores for that level? (e) Given that a player has not qualified for the bonus round, what is the probability that the player’s score on the first level was in the lowest 25% of scores for that level?

The table below summarizes baseline characteristics of patients participating in a clinical trial. a) Are there any statistically significant differences in baseline characteristics between treatment groups? Justify your answer.

The probability is0.45 that a traffic fatality involves an intoxicated or​ alcohol-impaired driver or nonoccupant. In

seven traffic​ fatalities, find the probability that the​ number, Y, which involve an intoxicated or​ alcohol-impaired driver or nonoccupant is

a. exactly​ three; at least​ three; at most three.

b. between two and four​, inclusive.

c. Find and interpret the mean of the random variable Y.

d. Obtain the standard deviation of Y.

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 54% at a level of significance of αα = 0.01. According to your sample, 38 out of 61 potential voters prefer the Democratic candidate.

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:
   Ho: ? p μ  ? = ≠ < >   (please enter a decimal)   
   H₁: ? p μ  ? = > < ≠   (Please enter a decimal)

3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer reject accept fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly larger than 54% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 54%.
   • The data suggest the populaton proportion is significantly larger than 54% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 54%
   • The data suggest the population proportion is not significantly larger than 54% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 54%.
8. Interpret the p-value in the context of the study.
   • There is a 9.68% chance that more than 54% of all voters prefer the Democratic candidate.
   • If the sample proportion of voters who prefer the Democratic candidate is 62% and if another 61 voters are surveyed then there would be a 9.68% chance of concluding that more than 54% of all voters surveyed prefer the Democratic candidate.
   • There is a 9.68% chance of a Type I error.
   • If the population proportion of voters who prefer the Democratic candidate is 54% and if another 61 voters are surveyed then there would be a 9.68% chance that more than 62% of the 61 voters surveyed prefer the Democratic candidate.
9. Interpret the level of significance in the context of the study.
   • If the proportion of voters who prefer the Democratic candidate is larger than 54% and if another 61 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 54%.
   • If the population proportion of voters who prefer the Democratic candidate is 54% and if another 61 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is larger than 54%
   • There is a 1% chance that the earth is flat and we never actually sent a man to the moon.
   • There is a 1% chance that the proportion of voters who prefer the Democratic candidate is larger than 54%.

In an introductory statistics class, there are 18 male and 22 female students. Two students are randomly selected (without replacement).

(a) Find the probability that the first is female

(b) Find the probability that the first is female and the second is male.

(c) Find the probability that at least one is female

---------------

I know that this question has to use the counting method, but i got confuse with how to start because i have to now find the probability of FIRST being a female, etc. Please provide workings with explanations alongside. Thank you in advance!

A scatterplot is the best way to show the mode of a categorical variable. (True/False)

An observational study with a convenience sample provides the strongest evidence that a predictor causes an outcome. (True/False)

Given a normal distribution, find the percentage of observed records that will be within 1.5 standard deviations (1.5 standard deviation to the left AND right of the mean). Show calculations and/or R code used to find your answer.

1. A composites manufacturer is having serious problems with porosity in their parts. A Quality Engineer samples 300 parts and finds 58 defective.

1. Test the hypothesis that defective rate (proportion defective) exceeds 15%. Test at a = 0.05.

What is the parameter of interest?   What assumptions are made? Show mathematical evidence to support assumption.

i. Write the null and alternative hypotheses.

ii. Calculate the test statistic.

iii. Determine the reject region. Find the p-value. Show normal graph including reject region and test statistic.

iv. Make a decision and write a thorough interpretation in context of the problem.

v. If in reality the true proportion defective is 12%, what type of error, if any, occurred?

2. Compute the power of the test if the true defective rate is 0.18.
3. Suppose that you wanted to reject the null hypothesis with probability at least 0.9 if true defective rate p = .18. What sample size should be used?
4. Construct a 95% Confidence Interval for p, the true proportion defective.

( PLEASE SHOW ALL YOUR WORK). I

MPORTANT NOTE: Make sure you do the following: -State Ho and Ha using notation for each hypothesis test conducted. -Use α= 0.05 for all hypothesis tests conducted. -Explain all results obtained for both hypothesis tests and confidence intervals.

You will need your ticker code (company abbreviation) for stock prices for this question. Use your ticker code to obtain the closing prices for the following two time periods to obtain two data sets:

March 2, 2019 to March 16, 2019

Data set A

February 16, 2019 to February 28, 2019

Data set B

Take the closing prices from data set B and add 0.5 to each one of them. Treat data sets A and B as hypothetical sample level data on the weights of newborns whose parents smoke cigarettes (data set A), and those whose parents do not (data set B).

a) Conduct a hypothesis test to compare the variances between the two data sets.

b) Conduct a hypothesis to compare the means between the two data sets. Selecting the assumption of equal variance or unequal variance for the calculations should be based on the results of the previous test.

c) Calculate a 95% confidence interval for the difference between means