Student Life: Employment Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full time jobs. A random of 81 students shows that 39 have jobs. Do the data indicate that more than 35% of the students have jobs? (Use a 5% level of significance.)

1. What is the level of significance? State the null hypothesis and alternate hypotheses.
2. Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
3. Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value
4. Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
5. Interpret your conclusion in the context of the application.

Note: For degrees of freedom d.f. not in the Student’s t table, use the closing d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more conservative answer. Answers may vary due to rounding.

A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 12 nursing students from Group 1 resulted in a mean score of 47.5 with a standard deviation of 7.8. A random sample of 15 nursing students from Group 2 resulted in a mean score of 54.7 with a standard deviation of 5.4. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.

: Determine the decision rule for rejecting the null hypothesis H0H0. Round your answer to three decimal places.

Decide whether each of the following statements is either true or false. You MUST explain your reasoning.

(a) If in a population, the shortest person is 1.5 metres tall and the tallest person is 2 metres tall, then the average height is always closer to 1.75 metres than to 2 metres.

(b) If the correlation between two variables X and Y is positive, then Y is small (below the average Y value) whenever X is small (below the average X value).

(c) I have collected information on the ethnic origins and annual salaries of all University of Regina faculty members. A good way to display the relationship between ethnic origin and annual salaries is with a scatterplot.

(d) Suppose that I take a simple random sample of University of Regina students and construct a 95% confidence interval for the mean IQ of all U of R students. My confidence interval is 110 ± 3. Now I want to use the same data to conduct a level α = 0.01 significance test of H0: the mean IQ of all U of R students is 112, against the alternative Ha: the mean IQ of all U of R students is not 112. Based on the confidence interval, I would reject H0.

Question 1

The probability that a teacher will see 0, 1, 2, 3, or 4 students

(a)        What is the probability that the teacher see 3 students?                                              

(b)       What is the probability that the number of students the teacher will see is between 1 and 3 inclusive?         

(c)        What is the expected number of students that the teacher will see?

(d)       What is the standard deviation?

Question 2

The probability that a house in an urban area will be burglarized is 5%. A sample of 50 houses is randomly selected to determine the number of houses that were burglarized.

(a)        Define the variable of interest, X.                                                      

(b)       What are the possible values of X?                                                    

(c)        What is the expected number of burglarized houses?                                    

(d)       What is the standard deviation of the number of burglarized houses?                      

(e)        What is the probability that none of the houses in the sample was burglarized?

Question 3

A sales firm receives an average of three calls per hour on its toll-free number. Suppose you were asked to find the probability that it will receive at least three calls, in a given hour:

(a) (i)   which distribution does this scenario fit and why?                           

    (ii) define the variable of interest, X.                                                       

    (iii) what are the possible values of X?                                                     

(b)       What is the probability that in a given hour it will receive at least three calls?

A recent national survey found that high school students watched an average (mean) of 7.2 movies per month with a population standard deviation of 0.7. The distribution of number of movies watched per month follows the normal distribution. A random sample of 47 college students revealed that the mean number of movies watched last month was 6.2. At the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students?

1. State the null hypothesis and the alternate hypothesis.

• H₀: μ ≥ 7.2; H₁: μ < 7.2

• H₀: μ = 7.2; H₁: μ ≠ 7.2

• H₀: μ > 7.2; H₁: μ = 7.2

• H₀: μ ≤ 7.2; H₁: μ > 7.2

2. State the decision rule.

• Reject H₁ if z < –1.645

• Reject H₀ if z > –1.645

• Reject H₁ if z > –1.645

• Reject H₀ if z < –1.645

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

4. What is your decision regarding H₀?

• Reject H₀

• Do not reject H₀

5. What is the p-value? (Round your answer to 4 decimal places.)

Chapter 18 Lead Question Discussion Post

The Teddy Bear Company operates a day-care facility. The variable cost of operations is $200 per child per month. The fixed costs amount to $3,200 per month. Teddy Bear charges $600 per child per month for their services. Although the Teddy Bear Company has the capacity to handle 32 children, the current number of children served is only 10.

The manager has operated the business out of her checkbook with few other accounting records. However, she is now desperate for some information. What is the Teddy Bear Company’s current monthly profit? What will their monthly profit be if they lose two students? The manager believes that it may be possible to double their students from the current level of 10 students per month to 20 students per month. To achieve this increase in volume, the manager will need to spend an additional $500 in fixed costs for promotional activities each month. Should the manager proceed with the promotional activities? Is the manager's plan a good idea?

Required:

Prepare a report to the manager responding to each of her questions. Use cost volume profit concepts in developing your response.

At a very large university, the mean weight of male students is 197.3 pounds with a standard deviation of 15.2 pounds. Let us assume that the weight of any student is independent from the weight of any other student. Suppose, we randomly select 256 male students from the university and look at the weight of each student in pounds. Let M be the random variable representing the mean weight of the selected students in pounds. Let T = the random variable representing the sum of the weights of the selected students in pounds.

a) What theorem will let us treat T and M as normal random variables?

Central Limit Theorem

Monte Carlo Theorem

Chebychev's Theorem

Law of Large Numbers

Convolution Theorem

b) What is the expected value of T?

c) What is the standard deviation of T?

d) If TK is T measured in kilograms (use 1kg = 2.2 pounds), then what is the standard deviation of TK?

e) What is the approximate probability that T is greater than 51,200?

f) What is the standard deviation of M?

g) What is the approximate probability M is between 197 and 198?

h) What is the approximate probability that T is within 2 standard deviations of its expected value?

Note: You need to show your work. If you choose to use Excel for your calculations, be sure to upload your well-documented Excel and to make note in this file how you arrived at your answers. If you choose to do the work by hand, Microsoft Word has an equation editor. Go to “Insert” and “Equation” on newer versions of Word. On older versions, go to “Insert” and “Object” and “Microsoft Equation.”

Chapter 8 Reflection:

The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 colleges students was used in this study.

1. Provide a 95% confidence interval for the population proportion of college students who work to pay for tuition and living expenses.

2. Provide a 99% confidence interval for the population proportion of college students who work to pay for tuition and living expenses.
3. What happens to the margin of error as the confidence is increased from 95% to 99%? Explain why this makes sense.

4. Suppose the NCES would like to re-do their study. If they want a 95% confidence interval with a margin of error for the population proportion within ±0.03, determine the sample size they should use. Use p*=0.47, the sample proportion from their previous study.

1. In Spring 2019, a local community college decided to switch textbooks for their calculus courses. In order to compare how students fared with the new book compared to the old book, a professor recorded the average grades that the students received on their exams. The average exam scores of 17 randomly selected students are shown below. State the 5-number summary by clearly labeling each value and create a boxplot for this data.

4. A statistics professor gave a final exam to his students where the first page consisted entirely of 12 true/false questions. Assume that a student decided to randomly guess on all 12 true/false questions on the first page. Use this data to answer the following questions.

1. Find the probability that this student guesses all 12 correctly

2. Find the probability that this student guesses at least 6 correctly

3. Find the probability that this student guesses exactly 7 correctly

4. Find the probability that this student guesses between 5 and 10 questions correctly.

5. Find the probability that this student guesses no more than 10 questions correctly.

Children in elementary schools in a US city were given two versions of the
same test, but with the order of questions arranged from easier to more
difficult in version A and in reverse order in version B. A randomly selected
group of 44 students were given version A; their mean grade was 83 with
standard deviation 5.6. Another randomly selected group of 38 students were
given version B; their mean grade was 81 with standard deviation 5.3.
A hypothesis test is to be performed to investigate whether the population
mean grade of students answering version A is the same as the population
mean grade of students answering version B.
(a) Name the hypothesis test that is appropriate to use in this situation.
(b) Using appropriate notation, which you should define, specify the null
and alternative hypotheses associated with the test.
(c) Calculate, by hand, the value of the estimated standard error of the
difference between the sample means.
(d) Calculate, by hand, the value of the test statistic.
(e) The sample sizes are both greater than 25, so you can assume that when
the null hypothesis is true, the test statistic follows (approximately) the
standard normal distribution. Complete the hypothesis test, carefully
detailing the conclusions of the test.