In order to compare the means of two populations, independent random samples of 400 observations are selected from each population with the following results:

To test the null hypothesis H₀: µ₁ - µ₂ = 0 versus the alternative hypothesis H_a: µ₁ - µ₂ ╪ 0 versus the alternative hypothesis at the 0.05 level of significance, the most accurate statement is

The value of the test statistic is 2.80 and the critical values are +1.645 and -1.645

The value of the test statistic is 2.80 and the critical values are +1.96 and -1.96

The value of the test statistic is 3.29 and the critical value is +1.645

The value of the test statistic is 3.29 and the critical values are +1.645 and -1.645

The value of the test statistic is 2.80 and the critical value is +1.96

If x is a binomial random variable, compute ?(?) for each of the following cases:

(a)  ?(?≤1),?=3,?=0.4

?(?)=

(b)  ?(?>1),?=4,?=0.2

?(?)=

(c)  ?(?<2),?=4,?=0.8

?(?)=

(d)  ?(?≥5),?=8,?=0.6

?(?)=

QUATION 2 PLEASE

1) The average female bobcat weight about 9.6 kg. Let's assume μ = 9.6 and σ = 1.65kg. a) Calculate Pr{Y > 10.3} b) Now assume you have a sample of n = 26 male bobcats. Calculate Pr{ Ȳ > 10.3}. c) Which probability is lower? Why? 2) Refer to problem 1. Now assume you take a sample of n = 4 male bobcats. a) What is the probability of the sample average being within 0.75 kg of the population mean (9.6 kg)? In other words, you need to figure out Pr{ μ - .75 < Ȳ < μ + .75} b) What is the probability of the sample average being within 0.75 kg of the population mean if the population mean is actually μ = 10.8 kg? Are you surprised? Why or why not? You should make sure you understand what happened here. c) Now assume a sample of n = 26 male bobcats and repeat (a). What is the effect of sample size?

7) Construct a 90% confidence interval for B1 when B1 = -8.4 , SSE = 4146 SSxx = 64 and n = 24 .Interpret the interval

A random sample of size 40 is selected from a population with the mean of 482 and standard deviation of 18. This sample of 40 has a mean, which belongs to a sampling distribution.

a) Determine the shape of the sampling distribution b) Find the mean and standard error of the sampling distribution

c) Find the probability that the sample mean will be between 475 and 495?

d) Find the probability that the sample mean will have a value less than 478?

e) Find the probability that the sample mean will be within 5 units of the mean?

A hairdresser collected data on the number of services provided on Saturdays and on weekdays. Her results are listed below. Assume the two samples were independently taken. Saturday: n1=60 and x1=24 Weekday: n2=45 and x2=15

a) Estimate the difference in the true proportions with a 99% confidence interval.

b) Interpret this interval, in sense what can you conclude about the true difference between these two proportions.

1) Average
2) Medium
3) Q1
4) Q3
5) P63
6) P93
7) Range
8) Variance
9) Standard Deviation
10) Construct a box-mustache graph for the above data.

a.If n = 21, x¯ = 44, and s = 10, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places. =    < u <

b.Assume that a sample is used to estimate a population mean μ . Find the 80% confidence interval for a sample of size 1058 with a mean of 65.2 and a standard deviation of 10.1. Enter your answer as a tri-linear inequality accurate to 3 decimal places.=    < μ <

c. The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 63.1 for a sample of size 27 and standard deviation 13.5. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.= <μ<   

d. Assume that a sample is used to estimate a population proportion p. Find the 98% confidence interval for a sample of size 209 with 21% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.
CI=

e. If n = 590 and X = 472, construct a 99% confidence interval for the population proportion, p. Give your answers to three decimals

We want to test H0 : µ ≥ 200 versus Ha : µ < 200 . We know that n = 324, x = 199.700 and, σ = 6. We want to test H0 at the .05 level of significance. For this problem, round your answers to 3 digits after the decimal point.

1. What is the value of the test statistic?

2. What is the critical value for this test?

3. Using the critical value, do we reject or not reject H0?

4. What is the p-value for this test?

5. Using the p-value, do we reject or not reject H0?

A researcher has studied subjects’ ability to learn to translate words into Morse code. He has experimented with two treatment conditions: in one condition, the subjects are given massed practice; they spend 6 full hours on the task. In the other condition, subjects are given distributed practice; they also spend 6 hours, but their practice is spread over four days, practicing 2 hours at a time. After the practice, all subjects are given a test message to encode; the dependent variable is the number of errors made. The researcher has matched the subjects on intelligence. The results are in the following table. Decide which statistical test would be appropriate, carry out the test, and evaluate the outcome. Assume a significance level of .05and that the direction of the outcome has not been What are we dealing with here? T test…. what must you do with the null hypothesis guys (accept or reject)? Massed Practice Distributed Practice S1 6 S1 5 S2 4 S2 3 S3 3 S3 2 S4 5 S4 2

Given the data on scores of students final grade in statistics (in percent) determine the following statistics.

43           45           48           51           53           54           57           59           60           60           60           60           61

70           70           71           71           72           72           72           75           76           76           79           81           81

83           85           87           88           88           89           89           91           92           93           96           98           98

99           100         101         101

1.       Create a relative frequency distribution table and histogram to determine the percentage of students getting a particular grade in statistics class. Do this by separating into 7 different classes by using 40’s, 50’s, 60’s, 70’s, 80’s, 90’s, 100’s. This will essentially be a table and graph of the probability distribution for final grade.

2.       Determine the following

a.       What is the probability of having a final score below 60?

b.       What is the probability of having a final score between 60 and 90?

c.        What is the probability of having a final score above 70?

We color each of the 99 numbers 1, 2, ..., 99 either red or green. We say that a coloring is good if there are more red numbers from 1 to 50 than red numbers from 51 to 99.

A. How many different colorings of these 99 numbers are there?

B. How many different good colorings of these 99 numbers are there?

I dont think the other answered solution is clear/correct. Please answer it correctly and explain. Thanks

We consider data in the following table, summarizing sales of a product (in thousands). For each of the questions, justify your answer.

(3.1) Assuming the given time-series shows evidence of seasonality, Determine the estimate sales values. (5)

A research conducts a study to determine whether there is an association between time students spent on revising the exam and level of level of exam anxiety among undergraduate. The researcher recruited 10 nursing students. To help the researcher, you need to do the hand calculation and then you use the SPSS

1. A worldwide fast food chain was bought out in a hostile takeover. Longtime customers are suspicious that the new owners have changed the chain’s famous “Big Bucket o’Fries” and don’t include the same number of fries. Prior to the takeover, the average number of fries included was 40 (SD = 3). These loyal customers with too much time on their hands purchased 9 buckets and counted the number of fries in each (before scarfing them down), here are their numbers: 38 42 37 49 36 39 43 36 35
   1. What is the null hypothesis?
   2. What is the alternative hypothesis?
   3. What test statistic will you use? Why?
   4. What alpha level will you set?
   5. What is the set up for the test statistic (i.e., write out the formulas needed with the appropriate numbers from the problem/show the initial steps)?
   6. What is the value of the test statistic?
   7. What is the p-value?
   8. What is your decision about the null hypothesis?
   1. What is your interpretation of the results?