1) A group of 41 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73.

The group of 41 students in the study reported an average of 4.44 drinks per with a standard deviation of 3.55 drinks.

Find the p-value for the hypothesis test.

The p-value should be rounded to 4-decimal places.

2) Commute times in the U.S. are heavily skewed to the right. We select a random sample of 520 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample, the mean commute time is 28.1 minutes with a standard deviation of 19.2 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.

What is the p-value for this hypothesis test?

(Your answer should be rounded to 4 decimal places.)

3) Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence to show that this is not true at her university. A random sample of 34 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 34 students studied each week was 17.9 hours. The sample standard deviation of 4.6 hours.

Find the p-value.

The p-value should be rounded to 4-decimal places.

Question1

A university lecturer is interested in comparing the engagement levels of first-year statistics students. In a previous nation-wide study, engagement levels of all university students were found to be normally distributed, with µ=60.00. The lecturer collects a random sample of 50 first-year students and the following statistics are obtained: M=65.43, SD=7.82.

What statistical procedure should be used, to test whether there is a significant mean difference in engagement levels between the lecturer’s first year students and the population average?

Question 2

A university lecturer is interested in comparing the enthusiasm levels of first-year statistics students. In a previous nation-wide study, enthusiasm levels were found to be normally distributed, with µ=70.00, σ=5.00. The lecturer collects a convenience sample of 50 first-year students and finds that her students have a mean enthusiasm level equal to 65.24.

What statistical procedure should be used, to test whether there is a significant mean difference in enthusiasm levels between the lecturer’s first year students and the population average?

Question 3

An organisational psychologist hypothesised that employee IQ levels of major Australian banks differ significantly to the general population. To test this, he performed a Z-test. Listed below are the IQ scores of 20 random employees:

105, 98, 103, 115,116,118,121,132,95,105,108,132,114,118,126,127,127,124,119,138.

If IQ scores are normally distributed, with µ=100, σ=15, what is the Z-statistic? Use these figures to calculate and select the correct the Z-statistic below.

Assume that a simple random sample has been selected and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Listed below are brain volumes in cm3

of unrelated subjects used in a study. Use a 0.05

significance level to test the claim that the population of brain volumes has a mean equal to

1099.2cm3.

A medical researcher says that less than

2323​%

of adults in a certain country are smokers. In a random sample of

200200

adults from that​ country,

16.516.5​%

say that they are smokers. At

alphaαequals=0.050.05​,

is there enough evidence to support the​ researcher's claim? Complete parts​ (a) through​ (e) below.​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

What is the​ claim?

A.Less than

2323​%

of all adults are smokers.

B.Less than

2323​%

of adults in the country are smokers.

C.Exactly

16.516.5​%

of all adults are smokers.

D.Exactly

16.516.5​%

of adults in the country are smokers.Identify

Upper H 0H0

and

Upper H Subscript aHa.

Upper H 0H0​:

p

▼

greater than>

greater than or equals≥

less than or equals≤

less than<

nothing

Upper H Subscript aHa​:

p

▼

greater than or equals≥

not equals≠

less than or equals≤

less than<

greater than>

nothing

​(Type integers or​ decimals.)

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

The critical​ value(s) is/are

z 0z0equals=nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

What​ is/are the rejection​ region(s)? Select the correct choice below and fill in the answer​ box(es) to complete your choice.

​(Round to three decimal places as​ needed.)

A.

zless than<nothing

and

zgreater than>nothing

B.

zgreater than>nothing

C.

zless than<nothing

​(c) Find the standardized test statistic z.

zequals=nothing

​(Round to two decimal places as​ needed.)

​(d) Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

▼

Fail to reject

Reject

Upper H 0H0.

There

▼

is not

is

enough evidence at the

55​%

level of significance to

▼

support

reject

the​ researcher's claim that

▼

less than 23%

exactly 16.5%

of

▼

adults in the country

all adults

are smokers.

Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of patients with SAD to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor mood) to 9 (improved mood). The hypothetical results are given in the following table.

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)

State the decision for the main effect of the time of day.

Retain the null hypothesis.Reject the null hypothesis.     

State the decision for the main effect of intensity.

Retain the null hypothesis.Reject the null hypothesis.     

State the decision for the interaction effect.

Retain the null hypothesis.Reject the null hypothesis.     

Summarize the results for this test using APA format.

Calculate the sample standard deviation and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

Class Frequency
61 - 66 4
67 - 72 8
73 - 78 5
79 - 84 7
85 - 90 13

1. A racing team owner wants to attempt to qualify his car for a major auto race. The owner believes that it will take a mean qualifying speed of over 223 mph to qualify for the race. During the two days of testing prior to qualifying, the team conducted 10 practice qualifying runs. The mean speed of these qualifying runs was 224.5 mph, with a standard deviation of .75 mph. Based on this information, does the owner have reason to believe that his car will qualify for the race, with at least 95% confidence. Assume all normality conditions apply. Solve using the p-value approach.

1. State the null hypothesis

2. State the alternative hypothesis

3. State the significance level.

4. Perform the calculations.

Suppose you are tossing a fair coin. You will keep tossing until you get two consecutive
heads. Let, X represents the number of tosses you will need. So the minimum value of X is
two.
(a) Using hand calculation, calculate P[X = 2], P[X = 3], P[X = 4] and P[X = 5].
(b) How to write an R function that keeps tossing the fair coin until two consecutive heads
show up and returns the total number of tosses. (run this function 1000 times)

Andrew surveyed a random sample of 500 Honolulu citizens on their attitudes toward legalizing marijuana use on a 7-point scale (1 strongly oppose, 4 neutral, 7 strongly support). The mean response of this sample of respondents is 4.4, and standard deviation (SD) is 2.5.

Assume that 4 indicates a neutral attitude. Can Andrew can claim that Honolulu citizens are on average in favor of legalizing marijuana use at 95% confidence level?

A 2007 Carnegie Mellon University study reported that online shoppers were willing to pay, on average, more than an extra $0.60 on a $15 purchase in order to have better online privacy protection.
A sample of n=22n online shoppers was taken, and each was asked how much extra would you pay, on a $15 purchase, for better online privacy protection?'' The data is given below, in $'s.

0.79,0.41,0.67,0.67,0.83,0.76,0.55,0.92,0.61,0.57,0.54,1.25,0.70,0.85,0.59,0.59,0.90,0.67,0.62,0.67,0.44,0.500.79,0.41,0.67,0.67,0.83,0.76,0.55,0.92,0.61,0.57,0.54,1.25,0.70,0.85,0.59,0.59,0.90,0.67,0.62,0.67,0.44,0.50

(a) Do the data follow an approximately Normal distribution? Use alpha = 0.05.  ? yes no

(b) Determine the PP-value for this Normality test, to three decimal places.
P=

(c) Choose the correct statistical hypotheses.
A. H0:μ=0.60HA:μ>0.60H0:μ=0.60HA:μ>0.60
B. H0:X¯¯¯¯=0.60,HA:X¯¯¯¯<0.60H0:X¯=0.60,HA:X¯<0.60
C. H0:μ>0.60HA:μ=0.60H0:μ>0.60HA:μ=0.60
D. H0:X¯¯¯¯=0.60,HA:X¯¯¯¯>0.60H0:X¯=0.60,HA:X¯>0.60
E. H0:μ=0.60,HA:μ≠0.60H0:μ=0.60,HA:μ≠0.60
F. H0:μ>0.60,HA:μ<0.60H0:μ>0.60,HA:μ<0.60


(d) Determine the value of the test statistic for this test, using two decimals in your answer.
Test Statistic =
(e) Determine the P-value for this test, enter your answer to three decimals.
P=

(f) Based on the above calculations, we should  ? reject not reject  the null hypothesis. Use alpha = 0.05

According to a PARADE poll of 1200 Americans, 75% of the respondents claimed that they had changed their behavior I an attempt to lower their risks of heart disease.  Assume that these 1200 people represent a random sample.  

a.) find a 98% confidence interval for the percentage of all Americans who say that they have changed their behavior to lower their risks of heart disease.

15. A researcher wants to know the poverty rate for the state of Kansas. The researcher randomly selects 150 families and finds 25 are at or below the poverty line.

a) Determine a 95% confidence interval for the proportion. State this interval below within an interpretive sentence tied to the given context.

b) The poverty rate for the US is stated to be 12.3%. Is there evidence at the 95% confidence level that the the poverty rate is higher than 12.3%? Explain your reasoning.

Explain the statistical concept of regression or reversion to the mean and provide an example.

A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Identify the simple events comprising the event (A and B). Select one: {1, 2, 3, 4, 5, 6} {2, 4, 6, 8, 10} IncorrectIncorrect {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} {2, 4, 6} Question 10 Incorrect 0.00 points out of 1.00 Not flaggedFlag question Question text A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Identify the simple events comprising the event (A or B). Select one: {1, 2, 3, 4, 5, 6, 8, 10} {1, 2, 3, 4, 5, 6, 7, 8, 10} {1, 2, 3, 4, 5, 6} IncorrectIncorrect {2, 4, 6}