A class contains 200 students. The teacher wants to test whether the mean IQ in the class exceeds 120. He chooses a random sample of 16 students and finds that the mean IQ in the sample is 122.8 and the standard deviation of the IQ’s in the sample is 10.9.

Let alpha = 0.05. You may assume that IQ's are Normally distributed. Which one of the following is the correct conclusion for this hypothesis test?

Group of answer choices

A Do not reject Ho. The p-value is less than the significance level.

B Reject Ho. The p-value is less than the significance level.

C Reject Ho. The p-value is not less than the significance level.

D Reject Ho simply because the sample mean is greater than 120.

E Do not reject Ho. The p-value is not less than the significance level.

The population of all Harvard students spends an average of $330 per semester on books. The population standard deviation of this expenditure is $65. A simple random sample of 40 students who attend the college is taken.

a. Provide the sampling distribution for the sample mean. Can you assume a normal distribution for the sample mean? Why or why not?

b. Calculate the probability that the average expenditure for the 40 students in the sample is between $320 and $350.

c. Calculate the probability that the average expenditure for the 40 students in the sample is less than $300.

d. If we increase the sample size to 50, show and explain what happens to the standard error. Without showing calculations, how would this change in sample size affect the probabilities you calculated in both b and c? Be specific.

1. For the Scale below what is the reliability scale reliability? Please explain if this is or is not appropriate and why?

2. , After reviewing the items on the scale, could there have been improvements to the scale to increase the reliability (i.e., item construction, length of scale, clarity of items)?

The Scale below ask how you live on a day-to-day basis. Please identify to what extent you agree or disagree with each statement.   Using the following;
Strongly Disagree Disagree Neither Disagree nor Agree Agree Strongly Agree

I would like to explore strange places. SD D N A SA
I would like to take a trip without planning where I’m going. SD D N A SA
I like to do scary things. SD D N A SA
I would like to try bungee jumping. SD D N A SA
I like wild parties. SD D N A SA
I like new and exciting experiences, even if I have to break the rules. SD D N A SA
I get restless when I spend too much time at home. SD D N A SA

True/False. a. _______ If the alternative (research) hypothesis Ha is accepted at the .05 level of significance, then it would also be accepted at the .10 level of significance. b. _______ If the null hypothesis Ho is not rejected, one can conclude that Ho is true. c. _______ When the power of a hypothesis test decreases, the probability of making a Type II error increases. d. _______ If the null hypothesis Ho is rejected, then the results are considered statistically significant. e. _______ Increasing sample sizes tends to decrease the widths of confidence intervals. f. ________ Decreasing the level of confidence tends to decrease the widths of confidence intervals.

Test at α =.05 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 400 students, 216 favor the system?

A set of final examination grades in an introductory statistics course was found to be normally distributed with a mean of 73 and a standard deviation of 8.

What is the probability of getting a grade of 79 or less?

What percentage of students scored between 61 and 81?

What is the probability of getting a grade no higher than 72 (less than 72) on this exam?

Suppose that the probability that a passenger will miss a flight is 0.0993. Airlines do not like flights with empty​ seats, but it is also not desirable to have overbooked flights because passengers must be​ "bumped" from the flight. Suppose that an airplane has a seating capacity of 50 passengers. ​(a) If 52 tickets are​ sold, what is the probability that 51 or 52 passengers show up for the flight resulting in an overbooked​ flight? ​(b) Suppose that 56 tickets are sold. What is the probability that a passenger will have to be​ "bumped"? ​(c) For a plane with seating capacity of 53 ​passengers, how many tickets may be sold to keep the probability of a passenger being​ "bumped" below 5​%?

1. In general, such establishments are appealing to higher-income households, while they are less appealing to lower-income households. Is this pattern the case for the Hobbit Hole?

I think I'm suppose to use ANOVA in excel to test this but I am not sure.

This is my data:

400 people were surveyed.

1. Household Earning< $15,000 26 people

2. Household Earning $15,000-$24,999 34 people

3. Household Earning $25,000-$49,999 82 people

4. Household Earning $50,000-$74,999 133 people

5. Household Earning $75,000-$99,999 16 people

6. Household Earning $100,000-$149,999 43 people

7. Household Earning $150,000+ 66 people

Ten healthy adult subjects were asked to walk on a treadmill while connected to monitors. One of two kinds of disturbances was applied during the walk, and the number of steps until adaptation was recorded. Each subject experienced both kinds of disturbance, in random order. Researchers want to know whether there is significant evidence of a different mean adaptation time (in steps) for the two disturbances. Here are the summary data for these 10 subjects:

1. (a) What is the research hypothesis?

2. (b) Give the null and alternative statistical hypotheses.

3. (c) Compute t

4. (d) The p-value of computed t is:

5. (e) Decision: reject or fail to reject H0

6. (f) Conclusion: What does this mean with regard to the research hypothesis?

The following data from a random sample represents the average daily energy intake in kJ for each of eleven healthy women:

5260    5470     5640     6180     6390     6515     6805     7515     7515    8230     8770     

Interest centred on comparing these data with an underlying mean daily energy intake of 7725 kJ This was the recommended daily intake. Departures from this mean in either direction were considered to be of interest. Assuming that the population is normal and the population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of significance was conducted. The null hypothesis is H₀: m = 7725. In order to make a decision as to whether to accept or reject the null hypothesis, we need to compare the observed test statistic with the critical value. What is this critical value |t_a/2| ?

State and prove the Monotone Convergence Theorem for the local convergence in measure.

In a simple random sample of 150 households, the mean number of personal computers was 1.32. Assume the population standard deviation is σ = 0.41.

a. Construct a 95% confidence interval for the mean number of personal computers.

b. If the sample size were 100 rather than 150, would the margin of error be larger or smaller than the result in part (a)?

c. If the confidence level were 98% rather than 95%, would the margin of error be larger or smaller than the result in part (a)? (You do not have to calculate the confidence interval.)

3. A wire-bounding process is said to be in control if the mean pull strength is 10 pounds.
It is known that the pull-strength measurements are normally distributed with a standard
deviation of 2. 4 pounds. Periodically, a random sample of certain size are taken from
this process.
a) If the mean pull strength is indeed 10 pound, what is the probability that a randomly
selected sample results a pull strength of less than 7. 75 pounds?
b) If the mean pull strength is indeed 10 pound, what is the probability that a randomly
selected sample of 40 results a mean pull strength of less than 7. 75 pounds?
c) If the mean pull strength is indeed 10 pound, what is the probability that a randomly
selected sample of 7 results a mean pull strength of less than 7. 75 pounds?

A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 47 calls per hour. The service rate per line is 25 calls per hour.

1. What is the probability that 0, 1, 2, and 3 access lines will be in use? Round your answers to 4 decimal places.
   

   j	Pj
   0
   1
   2
   3

   
   
2. What is the probability that an agent will be denied access to the system? Round your answers to 4 decimal places.
   
   
   
3. What is the average number of access lines in use? Round your answers to 4 decimal places.
   
   L =
   
4. In planning for the future, management wants to be able to handle λ = 55 calls per hour; in addition, the probability that an agent will be denied access to the system should be no greater than the value computed in part (b). How many access lines should this system have?
   
   lines will be necessary.

A marketing research experiment was conducted to study the relationship between the length of time necessary for a buyer to reach a decision (y) and the number of alternative package designs (2, 3, or 4 designs). Remember that s = √MSE. Use the tables below to answer the following questions.

a) Predict the mean amount of time necessary for a buyer to make a decision if there were 5 package choices. Is this value meangingful? Why or not?
?̂ =  

The prediction   is/ is not  meaningful since ?0 = 5   does/ does not  fall within the range of   length of time/ designs .

b) Find the 95% prediction interval (i.e. confidence interval for predicting) of y when ?0x0 = 4.
?̂ =  
??/2 =  
(  ,  )

c) Is there evidence to support that the correlation coefficient is not equal to 0? Test using ?α = 0.05.
?0:? = < > /=  0
??:? = < > /= 0

Test statistic: t =  
Critical value: ??/2 =  
Decision:   Reject/ Fail to reject  
Interpretation: There   is/ is not  evidence to support that the correlation coefficient is not equal to 0.