1) As a stock analyst, your boss, Jerry, has asked you to compile some information on stock of Southern Infrastructure Corporation including a 95% confidence interval for the mean daily return that he needs to include in a report to senior management. He says that he is also not sure exactly what a 95% confidence interval means and would like you to add an explanation.

You have been following the share price of Southern Infrastructure Corporation and have recorded the daily return (as a percentage) for the last 120 days. The data is presented here:

0.853 0.486 0.608 0.119 1.355 1.133 1.314 2.113 0.903 1.008 -0.106 2.148

0.301 2.384 0.932 0.404 0.486 1.068 1.281 -0.281 1.398 1.612 1.965 1.747

2.101 1.645 2.64 2.536 1.993 0.833 -0.472 3.345 -0.219 0.943 2.907 0.13

2.82 -0.154 0.083 1.209 2.179 0.56 0.139 2.643 1.895 -0.311 1.494 1.77

-0.178 -1.678 1.427 0.376 2.409 -1.094 1.928 -0.032 1.964 0.335 1.046 1.402

0.995 0.116 0.021 2.279 0.465 1.787 2.025 1.166 1.35 1.608 1.089 -0.206

1.306 -0.094 -0.482 2.137 0.3 3.144 0.629 2.626 1.717 2.587 2.154 0.996

3.425 -0.545 0.213 -0.477 0.614 -0.726 -0.006 2.605 0.615 1.33 1.103 0.318

2.617 0.439 -0.03 -0.399 1.767 2.552 1.013 2.284 2.771 1.306 3.714 0.762

1.147 0.262 1.486 0.974 1.998 1.104 1.62 1.406 1.823 0.941 -0.252 2.968

Historically, the standard deviation in daily return for this stock is 1.0%.

Complete the report to your boss. Give your numeric answers to 3 decimal places.

Sent:August 7, 2021 11:10 AMTo:Jerry KendallSubject:Southern Infrastructure Corp. stock info

Dear Jerry,

Here are the results gathered from the collected data:

Assuming a population standard deviation in daily return of 1.0%, the 95% confidence interval for the mean daily return is:

a)______ _______

b)This means that:

A) approximately 95% of sample means will be within the interval given above

B) using a process that gives correct results in 95% of cases, the population mean daily return is within the interval given above

C) the population mean daily return is definitely within the interval given above

D) on approximately 95% of days in a given period the stock makes a return within the interval given above

Answer: _____

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8.6

2) The Mean Corporation manufactures a line of unassembled furniture. Based on historical evidence, the customer service manager knows that the proportion of customers that have not had any problems with assembling the furniture at home is 0.65.

Improvements have been made to the instructions provided with the furniture, and the customer service manager believes that this will increase the proportion of customers that can assemble the furniture without problems () to above 0.65. A hypothesis test is conducted in order to find out.

The null and alternative hypotheses are:

H₀:= 0.65

H_A:> 0.65

To run the test, the manager randomly selects a sample of 119 people and asks them to assemble a piece of furniture produced by the Mean Corporation. The proportion of people in this sample that succeed is 0.69. You may find thisstandard normal tableuseful throughout this question.

a)Calculate the test statistic (z). Give your answer to 2 decimal places.

z =______

b)Calculate the P-value. Give your answer as a decimal to 4 decimal places.

P =______

3) A psychologist has developed an aptitude test which consists of a series of mathematical and vocabulary problems. They want to test the hypothesis that the mean test score is 63.9.

A random sample of 40 people have taken the test and their results recorded:

67 72 96 64 55 59 58 68 65 61

49 78 83 62 54 72 43 85 78 87

75 57 90 69 46 55 63 84 97 79

55 96 51 75 77 67 88 43 62 62

You may find thisStudent's t distribution tableuseful throughout this question.

a)Calculate the test statistic (t) for the hypothesis test. Give your answer to 4 decimal places.

t =______

b) A level of significance of = 0.1is to be used for the test. The P-value for this test statistic isless or greaterthan the level of significance.

ANSWER: ______

c)The result of this test is that the null hypothesis isrejected or not rejected

ANSWER: __________

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9.1

4) This question relates to the patterns that occur when trying to draw inferences about one or two population means or population proportions. It is assumed in this question that any confidence intervals or tests will be completed using a t-distribution or the standard normal distribution.

In a hypothesis test for a population mean or proportion, or comparing two means or two proportions, the numerator of the test statistic will be:

A) the difference between a sample statistic and the hypothesized value of the relevant parameter

B) the true value of the relevant parameter

C) a sample statistic

D) the hypothesized value of the relevant parameter

E) the difference between a sample statistic and the true value of the relevant parameter

ANSWER:___________

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5) Two separate marketing teams, Team A and Team B, have each designed a 30 second advertisement for the new Cloak soft drink. The manager of marketing is interested to see if there is any difference between the effectiveness of the two ads.

A random sample of 50 people are shown the ad from Team A and asked if they would definitely buy the new drink. In this sample, 29 people said that they would. A second random sample of 50 people are shown the ad from Team B and asked if they would definitely buy the drink. In this sample, 13 people said that they would.

Let₁denote the population proportion of people that would definitely buy the drink if they saw the ad from Team A. Let₂denote the population proportion of people that would definitely buy the drink if they saw the ad from Team B.

A hypothesis test is conducted with the following hypotheses:

H₀:₁=₂

H_A:₁₂

The level of significance used in this test is 0.05. You may find thisstandard normal tableuseful.

a)Calculate the test statistic (z) for this test. Give your answer to 2 decimal places.

z =_________

b) In this test the null hypothesis is or is not rejected. ANSWER:____________

6) A computer training group would like to compare the effectiveness of two modes of training. The first mode of training is a short 20 minute interactive one-on-one tutorial with the participant and the second mode is a one hour video that the participant watches.

A random sample of 100 people are invited to take part in the tutorial, which is followed by a test to measure competency at the tasks covered. The proportion of people that pass this test (to 2 decimal places) is 0.44. Similarly, a random sample of 50 people are invited to watch the video, which is also followed by the same test. The proportion of people that pass this test (to 2 decimal places) is 0.60.

Let₁denote the population proportion of people that would pass the competency test after taking the tutorial. Similarly, let₂denote the population proportion of people that would pass the competency test after watching the video.

Construct a 95% confidence interval for the difference between these two proportions(₁-₂). Give your answers to 3 decimal places. You may find thisstandard normal tableuseful.

ANSWER:

__________₁-₂_________