7.4

1) Internet company Gurgle is carrying out testing on the efficiency of its search engine. A sample of 45 searches have been carried out and the time taken to display the results has been recorded for each search. The mean search time for the sample was calculated as 0.1500 seconds. The standard deviation of the search times for the sample was calculated as 0.0140 seconds. The population standard deviation of search times is unknown.

a)Select all the techniques that are commonly used to construct a confidence interval for the mean when the population standard deviation () is unknown:

A) Approximate the population standard deviation () with the sample standard deviation (s)

B) Replace the sample size (n) withn-1

C)Decrease the confidence level to compensate for the increased margin of error

D)Approximate the standard normal distribution with the Student's t distribution

ANSWERS:________

b)Calculate the upper and lower bounds of the 95% confidence interval for the mean search time for the Gurgle search engine. You may find thisStudent's t distribution tableuseful. Give your answers in seconds to 4 decimal places.

Upper bound =______ seconds

Lower bound =_______ seconds

------------------------------------------------------------------------------------------------------------------------------

2) A psychologist has developed an aptitude test which consists of a series of mathematical and vocabulary problems. They are interested in determining the mean score for the test.

A random sample of 31 people have taken the test and the mean test score for the sample is 75. The sample standard deviation for this group is 8.7.

Calculate the 95% confidence interval for the mean test score. You may find thisStudent's t distribution tableuseful. Give your answers to 2 decimal places.

________ ________

------------------------------------------------------------------------------------------------------------------------------

3)Tyler and Jack are both studying a numerical variable X. Both students want to estimate the population mean of this variable, and they each intend to collect a sample, calculate a sample mean and construct a 95% confidence interval. Each student will collect their own sample, but both samples will have 30 items in them.

When constructing his confidence interval, Tyler assumes a value for the population standard deviation, . In contrast, Jack does not assume a value for the population standard deviation. Jack calculates the sample standard deviation, s, and uses this in his confidence interval. However as it turns out, the sample standard deviation that Jack calculates turns out to be equal to the value assumed by Tyler for the population standard deviation.

Based on this information, it is true to say that:

A) it is impossible to tell which confidence interval will be wider

B) both confidence intervals will be of the same width

C) Tyler's confidence interval will be wider than Jack's

D) Jack's confidence interval will be wider than Tyler's

ANSWER:_______

------------------------------------------------------------------------------------------------------------------------------

7.5

4) A friend tells you that she has conducted a survey to find the proportion of people in her university that utilize the campus internet cafe at least once a day. She has collected a sample and calculated a sample proportion ofp = 0.47. She uses this value to calculate a confidence interval for the population proportion. Your friend says that she is not going to tell you the sample size or the level of confidence used in her construction, and wants you to guess what the confidence interval is. She gives you 5 options.

Select the interval(s) that, based on the information given, couldpossiblybe the confidence interval your friend calculated:

A) the interval between 0.37 and 0.67

B) the interval between 0.27 and 0.47

C) the interval between 0.37 and 0.57

D) the interval between 0.47 and 0.67

E) the interval between 0.27 and 0.57

ANSWERS:__________

5) A survey was run by a high school student in order to determine what proportion of mortgage-holders in his town expect to own their house within 10 years. He surveyed 159 mortgage holders and found that the proportion of these that did expect to own their house within 10 years is 0.67.

The student decides to construct a 95% confidence interval for the population proportion. You may find thisstandard normal tableuseful for the following questions.

a)Calculate the margin of error that the high school student will have. Give your answer as a decimal to 3 decimal places.

Margin of error =_______

A different high school student sees this survey and decides to try and repeat it. This second high school student also surveys 159 mortgage holders, but this student finds that the proportion of these that do expect to own their house within 10 years is 0.83. This student also constructs a 95% confidence interval for the population proportion.

b)Calculate the margin of error that the second student will have. Give your answer as a decimal to 3 decimal places.

Margin of error =______

A survey of 119 small business owners found that a proportion of 0.689 of the owners had decided to downsize in the year following the Global Financial Crisis (GFC).

a)Calculate the number of surveyed small business owners that downsized. Give your answer to the nearest whole number.

Number of owners that downsized =________

A 95% confidence interval is to be constructed for the proportion of all small business owners that decide to downsize after the GFC. You may find thisstandard normal tableuseful for the following questions.

b)Calculate the lower bound for the confidence interval. Give your answer as a decimal to 3 decimal places.

Lower bound for confidence interval =________

c)Calculate the upper bound for the confidence interval. Give your answer as a decimal to 3 decimal places.

Upper bound for confidence interval =________