STAT1122 Biostattistics

Assignment 2

Question 1 [Total: 12 marks]

Electric and magnetic fields (EMF) are part of the natural environment and are present in the earth’s core and atmosphere. These fields are also produced wherever electricity or electrical equipment is used. These fields come from the wires that transport electricity to our homes as well as all devices which use electricity in the home. Exposure to EMF has, in some studies, been linked with human health. One such link has been made with brain cancer.

The recommended magnetic field exposure limit over a 24 hour period is 1000 milligauss. Exposure to levels in excess of 1000 milligauss is considered high exposure.

Information was collected from a sample of 400 male adult subjects.

Of the total sample, 50 subjects were exposed to high levels of EMF.

Of the total sample, 30 subjects had a diagnosis of brain cancer.

Of those exposed to high levels of EMF, 42% had a diagnosis of brain cancer.

What is the probability of the following events. Show all working. No marks awarded for the correct answer without working out. Hint: A cross tabulation can help.

(a) A randomly selected male adult does not have brain cancer. [1 mark]

(b) A randomly selected male adult has a positive diagnosis of brain cancer given that he is

exposed to normal levels of EMF. [3 marks]

(c) A randomly selected adult male tests negative for brain cancer given that he is exposed to high levels of EMF. [3 marks] (d) What is the probability that an adult male has brain cancer and is exposed to high levels of EMF? [2 marks]

(e) Are the events “exposed to high levels of EMF” and “have brain cancer” independent?

Show your working. [3 marks]

Marking Criteria: You need to show all working. No marks awarded for the correct answer without working out. For full marks, you need to demonstrate understanding of the probability concepts involved in each part of this question as well as an answer expressed in an English sentence.

Question 2 [Total: 13 marks]

Social networking sites, for example Facebook, My Space and Black Planet, have grown in popularity as users create web pages loaded with music, photographs, and profiles. Hitwise reported that the mean time spent by a user at Facebook during April 2010 was 25 minutes. Suppose the distribution of time spent at Facebook per month is normally distributed, with a mean µ = 25 minutes and the standard deviation s = 4.0 minutes.

If a Facebook user is selected at random:

(a) Find the probability that the user spends less than 15 minutes per month at the site.

[2 marks]

(b) Find the probability that the user spends between 20 and 35 minutes per month at the site.

[3 marks]

(c) What is the amount of time per month a user spends on Facebook, if only 1% of users spend

this time or longer on Facebook? [4 marks]

(d) Between what values do the time spent of the middle 90% distribution of Facebook users fall? [4 marks]

Marking Criteria: You may use any of the tools that you have been shown to determine the necessary probabilities, but cutting and pasting from the tools is not an adequate answer. For full marks, you need to demonstrate understanding of the probability concepts involved in each part of this question. Calculation of relevant Z scores is expected as well as an answer expressed in an English sentence.

Question 3 Fungal Infection of Fish [Total: 10 marks]

A large fishing farm with thousands of fish has been treating its fish to stop a spreading fungal infection. In the past, the proportion of fish that being infected was 10%. There is a new claim that the proportion is now higher. A random sample of 200 fish is taken to determine the proportion p that is infected in this population. A careful examination determines that 24 of the fish sampled are infected.

(a) Construct a 90% confidence interval for the proportion of fish that being infected.

[3 marks]

(b) Use all steps for hypothesis testing to test the new claim that the proportion is now higher.

Use a significance level of 10%. [5 marks]

(c) What assumptions or conditions have you made in statistical inference in part (a)? Are

they being satisfied? [2 marks]

Marking Criteria: You need to show all working. No marks awarded for the correct answer without working out. For full marks, you need to demonstrate understanding of the statistical inference concepts involved in each part of this question as well as an answer expressed in an English sentence.

End of Assignment 2

Assignment 2

Question 1 [Total: 12 marks]

Electric and magnetic fields (EMF) are part of the natural environment and are present in the earth’s core and atmosphere. These fields are also produced wherever electricity or electrical equipment is used. These fields come from the wires that transport electricity to our homes as well as all devices which use electricity in the home. Exposure to EMF has, in some studies, been linked with human health. One such link has been made with brain cancer.

The recommended magnetic field exposure limit over a 24 hour period is 1000 milligauss. Exposure to levels in excess of 1000 milligauss is considered high exposure.

Information was collected from a sample of 400 male adult subjects.

Of the total sample, 50 subjects were exposed to high levels of EMF.

Of the total sample, 30 subjects had a diagnosis of brain cancer.

Of those exposed to high levels of EMF, 42% had a diagnosis of brain cancer.

What is the probability of the following events. Show all working. No marks awarded for the correct answer without working out. Hint: A cross tabulation can help.

(a) A randomly selected male adult does not have brain cancer. [1 mark]

(b) A randomly selected male adult has a positive diagnosis of brain cancer given that he is

exposed to normal levels of EMF. [3 marks]

(c) A randomly selected adult male tests negative for brain cancer given that he is exposed to high levels of EMF. [3 marks] (d) What is the probability that an adult male has brain cancer and is exposed to high levels of EMF? [2 marks]

(e) Are the events “exposed to high levels of EMF” and “have brain cancer” independent?

Show your working. [3 marks]

Marking Criteria: You need to show all working. No marks awarded for the correct answer without working out. For full marks, you need to demonstrate understanding of the probability concepts involved in each part of this question as well as an answer expressed in an English sentence.

Question 2 [Total: 13 marks]

Social networking sites, for example Facebook, My Space and Black Planet, have grown in popularity as users create web pages loaded with music, photographs, and profiles. Hitwise reported that the mean time spent by a user at Facebook during April 2010 was 25 minutes. Suppose the distribution of time spent at Facebook per month is normally distributed, with a mean µ = 25 minutes and the standard deviation s = 4.0 minutes.

If a Facebook user is selected at random:

(a) Find the probability that the user spends less than 15 minutes per month at the site.

[2 marks]

(b) Find the probability that the user spends between 20 and 35 minutes per month at the site.

[3 marks]

(c) What is the amount of time per month a user spends on Facebook, if only 1% of users spend

this time or longer on Facebook? [4 marks]

(d) Between what values do the time spent of the middle 90% distribution of Facebook users fall? [4 marks]

Marking Criteria: You may use any of the tools that you have been shown to determine the necessary probabilities, but cutting and pasting from the tools is not an adequate answer. For full marks, you need to demonstrate understanding of the probability concepts involved in each part of this question. Calculation of relevant Z scores is expected as well as an answer expressed in an English sentence.

Question 3 Fungal Infection of Fish [Total: 10 marks]

A large fishing farm with thousands of fish has been treating its fish to stop a spreading fungal infection. In the past, the proportion of fish that being infected was 10%. There is a new claim that the proportion is now higher. A random sample of 200 fish is taken to determine the proportion p that is infected in this population. A careful examination determines that 24 of the fish sampled are infected.

(a) Construct a 90% confidence interval for the proportion of fish that being infected.

[3 marks]

(b) Use all steps for hypothesis testing to test the new claim that the proportion is now higher.

Use a significance level of 10%. [5 marks]

(c) What assumptions or conditions have you made in statistical inference in part (a)? Are

they being satisfied? [2 marks]

Marking Criteria: You need to show all working. No marks awarded for the correct answer without working out. For full marks, you need to demonstrate understanding of the statistical inference concepts involved in each part of this question as well as an answer expressed in an English sentence.

End of Assignment 2

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