A survey was conducted to estimate the mean number of books (denoted by µ) each university student read in the last year. Among a random sample of 51 students, the number of books each student read in the last year was recorded. The sample mean was 8.039 and the sample standard deviation was 2.545.

a. Write down the point estimate of µ.

b. Calculate the standard error of the point estimate in a.

c. To construct a 95% two-sided confidence interval for µ, what’s the multiplier to use?

d. Calculate the lower endpoint of the 95% two-sided confidence interval for µ.

e. Calculate the upper endpoint of the 95% two-sided confidence interval for µ.

f. Consider a hypothesis testing problem where the null hypothesis is H0 : µ = 10 and the alternative hypothesis is Ha : µ 6= 10. Use a significance level of 0.05. Based on the 95% two-sided confidence interval for µ above, what’s your decision about whether to reject H0? Give a brief explanation.

g. Suppose you’re asked to conduct a hypothesis testing to show that on average a student read more than 5 books last year. Which pair of hypotheses should be used? (5 points) A. H0 : µ = 5 against Ha : µ 6= 5 B. H0 : µ < 5 against Ha : µ ≥ 5 C. H0 : µ ≤ 5 against Ha : µ > 5 D. H0 : µ ≥ 5 against Ha : µ < 5

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:

To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.

If the promotional budget is limited to $16,400, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? If required, round your answers to the nearest dollar.

What is the maximum total audience that would be reached? Round your answer to the nearest whole number.

By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number.

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 100; σ = 12

P(x ≥ 120)

Find the indicated probability using the standard normal distribution. P(0< z<0.455)

Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?

(b) Fill in the boxes. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)

1 2 3 4 This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Hypertension is defined as a blood pressure reading over 140 mm Hg systolic and/or over 90 mm Hg diastolic. Hypertension, if not corrected, can cause long-term health problems. In the college-age population (18–24 years), about 9.2% have hypertension. Suppose that a blood donor program is taking place in a college dormitory this week (final exams week). Before each student gives blood, the nurse takes a blood pressure reading. Of 196 donors, it is found that 29 have hypertension. A scientist claimed that these data indicate that the population proportion of students with hypertension during final exams week is higher than 9.2%. Use a 5% level of significance to test the claim.

1. Find the null and the alternative hypothesis.

2. Find the test statistic.

3. Would reject or fail to reject the null hypothesis? Explain.

4. Would you agree or disagree with the scientist’s claim?

A random sample was taken of 27 concrete beams produced by a certain manufacturer. Each beam in the sample was weighed (in Kg) to assess whether the concrete content was up to industry standards.Sample mean=68.4, Standard Deviation=2.6.

Construct a 95% confidence interval for the true average weight of concrete beams coming from this manufacturer. Interpret this confidence interval in the form of a sentence.The manufacturer claims that their manufacturing process is calibrated to produce average beam weights that satisfy the industry requirement of (at least) 69.5Kg per beam.Test the validity of the manufacturer’s claim using the data collected. Summarise your findings in the form of a probability statement, and write your conclusions in a way that is understandable to a quality control officer.Assess the validity of the assumptions needed to carry out the calculations.

Are medical students more motivated than law students? A randomly selected group of each were administered a survey of attitudes toward Life, which measures motivation for upward mobility. The scores are summarized below. The researchers suggest that there are occupational differences in mean testosterone level. Medical doctors and university professors are two of the occupational groups for which means and standard deviations are recorded and listed in the following table.

Let us denote:

• μ1:μ1: population mean testosterone among medical doctors,
• μ2:μ2: population mean testosterone among university professors,
• σ1:σ1: population standard deviation of testosterone among medical doctors,
• σ2:σ2: population standard deviation of testosterone among university professors.

If the researcher is interested to know whether the mean testosterone level among medical doctors is higher than that among university professors, what are the appropriate hypotheses he should test?
H0:μ1=μ2H0:μ1=μ2   against   Ha:μ1≠μ2Ha:μ1≠μ2.
H0:x¯1=x¯2H0:x¯1=x¯2   against   Ha:x¯1>x¯2Ha:x¯1>x¯2.
H0:x¯1=x¯2H0:x¯1=x¯2   against   Ha:x¯1<x¯2Ha:x¯1<x¯2.
H0:μ1=μ2H0:μ1=μ2   against   Ha:μ1>μ2Ha:μ1>μ2.
H0:x¯1=x¯2H0:x¯1=x¯2   against   Ha:x¯1≠x¯2Ha:x¯1≠x¯2.
H0:μ1=μ2H0:μ1=μ2   against   Ha:μ1<μ2Ha:μ1<μ2.

Case 1: Assume that the population standard deviations are unequal, i.e. σ1≠σ2σ1≠σ2.
What is the standard error of the difference in sample mean x¯1−x¯2x¯1−x¯2? i.e. s.e.(x¯1−x¯2)=s.e.(x¯1−x¯2)= [answer to 4 decimal places]

Rejection region: We reject H0H0 at 1% level of significance if:
t<−3.05t<−3.05.
t>3.05t>3.05.
t<−2.68t<−2.68.
t>2.68t>2.68.
|t|>3.05|t|>3.05.
None of the above.

The value of the test-statistic is: Answer to 3 decimal places.

If α=0.01α=0.01, and the p-value is 0.4335, what will be your conclusion?
There is not enough information to conclude.
Do not reject H0H0.
Reject H0H0.

Case 2: Now assume that the population standard deviations are equal, i.e. σ1=σ2σ1=σ2.
Compute the pooled standard deviation, spooledspooled [answer to 4 decimal places]

Rejection region: We reject H0H0 at 1% level of significance if:
t>3.05t>3.05.
t<−2.68t<−2.68.
t>2.68t>2.68.
|t|>3.05|t|>3.05.
t<−3.05t<−3.05.
None of the above.

The value of the test-statistic is: Answer to 3 decimal places.

If α=0.01α=0.01, , and the p-value is 0.4525, what will be your conclusion?
Reject H0H0.
Do not reject H0H0.
There is not enough information to conclude.

In a high school literature club, there are 3 groups: one is Novel, one in Poetry, and one in Comics. These sections are open to any of the 100 students in the school. There are 25 students in the Novel group, 31 in the Poetry group, and 19 in the Comics group. There are 18 students that are in both Novel and Poetry, 7 that are in both Novel and Comics, and 14 are in both Poetry and Comics. In addition, there are 5 students taking all 3 groups. If a student chosen at random,

a) the probability that he is not included in any of these groups is

b) the probability that he is playing exactly one literature group is

c) When two people are chosen randomly, the probability that at least 1 is included in a group is

You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case.

While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 91.1%.
(Report answer accurate to three decimal places with appropriate rounding.)

MY MATH İS TERRBİLE THAN YOU İMAGİNE. so can you summarize and show all the formulas and basic questions of all of them, I will upvote and I will pray for you:D Thank you

Hypothesis Tests of a Single Population

1)Formulate null and alternative hypotheses for applications involving

-a single population mean from a normal distribution

-a single population proportion (large samples)

-the variance of a normal distribution

2) Formulate a decision rule for testing a hypothesis

3) Know how to use the critical value and p-value approaches to test the null hypothesis (for both mean and proportion problems)

4) Use the chi-square distribution for tests of the variance of a normal distribution

in Other words:

1) hypothesis testing methodology

2) z Test for the mean (σ known)

3) critical value and p-value approaches to hypothesis testing

4) one-tail and two-tail tests

5) t test for the mean (σ unknown)

6) z test for the proportion

7) a hypothesis test for the variance (χ²

In Faroe island, a sports training camp provides 3 different sections: one in Squash, one in Football, and one in Basketball. These sections are open to any of the 100 people in the camp. There are 28 students in the Squash section, 26 in the Football section, and 16 in the Basketball section. There are 12 students that are in both Squash and Football, 4 that are in both Squash and Basketball, and 6 are in both Football and Basketball. In addition, there are 2 people taking all 3 sections. If a person chosen at random;

a) If a person chosen at random, the probability that he is not playing in any of these sports sections is

b) If a person chosen at random, the probability that he is playing exactly one sports section is

c) When two people are chosen randomly, the probability that at least 1 is playing in a sports section is

In a red box, there are 4 vanilla ice-cream and 8 chocolate ice-cream whereas in a blue box, there are 3 vanilla and 3 chocolate ice-cream. An ice-cream is randomly chosen from the red box and put into the blue box, and an ice-cream is then randomly selected from the blue box.

a) what is the probability that the ice-cream selected from blue box is a vanilla ice-cream

b)what is the conditional probability that the transferred one was chocolate ice-cream, given that a vanilla ice-cream is selected from the blue box

1. The general manager of the Hilton Hotel in Sydney is evaluating an employment screening test for the front office clerical staff. During this evaluation all new clerical employees are given the test. 70% pass the test; the rest fail. At a later time, after the new clerical employees have been working for a while, their performance is evaluated as being satisfactory or unsatisfactory. Historically, 80% of all clerical employees have been found to be satisfactory, and 75% of the satisfactory clerical employees in the evaluation of the employment screening test have passed the screening test. (a) From the given information, determine the probabilities of the following events: (i) passing the test, (ii) having satisfactory performance and (iii) passing the test given satisfactory performance. [3 marks] (b) Using your answers to part (a), determine the probability of a clerical employee passing the test and having satisfactory performance. [1 mark] (c) Using your answer in parts (a) and (b), determine the probabilities of the a clerical employee: (i) failing the test and having satisfactory performance, (ii) failing the test and having unsatisfactory performance, (iii) passing the test and having unsatisfactory performance, and (iv) having unsatisfactory performance. [4 marks] (d) Using your answers in part (c), determine the probabilities of a clerical employee: (i) failing the test given they are found to have unsatisfactory performance, (ii) failing the test given they are found to have satisfactory performance, (iii) passing the test given they are found to have unsatisfactory performance, (iv) unsatisfactory performance given they failed the test, (v) satisfactory performance given they passed the test, (vi) unsatisfactory performance given they passed the test, and (vii) satisfactory performance given they failed the test. [7 marks] (e) Using your answers in part (d), determine the following percentages: (i) clerical employees who failed the test and prove to be unsatisfactory, and (ii) clerical employees who passed the test and who prove to be satisfactory. [2 marks] (f) Government guidelines require screening tests to achieve at least 20% for part (i) in (e) and at least 60% for part (ii) in (e). Does this test meet those government requirements? Explain. [2 marks]

1. Complete the analysis of variance table for the following data. Treat it as a two way Block Design.  (Use α = 0.05). In each cee there are 2 observations. For example in cell 1,1 they are 13 and 1

DATA

ANOVA TABLE

State Ho and Ha for both sources of variability.

Source A   Ha:                                          Source B    Ha:

How many degrees of freedom for A? …….  What is the Critical Point for A?............

How many degrees of freedom for B? …….  What is the Critical Point for B?............

Do you reject Ho for Source A?  ……..                Do you reject Ho for Source B?  ……..

So, is Source A statistically significant? …………..      And Source B? ………………..