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QUESTION 10 Two types of material (A and B) are being tested for their ability to withstand different temperatures. A random selection of both materials was subjected to extreme temperature changes and then classified according to their condition after they were removed from the testing facility. The results are shown in the table. Material Broke completely Showed defects ot | 5 | 3| o T s s An approximate 95% confidence interval for the probability that material A will break completely or show defects is given by [c—l.% /w cfl.% /Mj n n The values of ¢ and » are @A) 9 andos 95 ®) Y andos 200 ©) 140 and9s 200 @) 9% and 200 200
QUESTION 17 (4 marks) In a survey of 326 lecturers 303 said that on at least one occasion a mobile phone had rung in a lecture they were giving. Determine the sample size required to conduct a follow-up survey that provides 95% confidence that this one-point estimate is correct to within + 0.02 of the population proportion.
QUESTION 20 (5 marks) Assuming the approximate normality of sample proportions (p and p ) and based on two independent samples the approximate confidence interval for the difference of two proportions is given by pd-p) p 1-p ) pd-p) p 0-p )) ————————— P =t i B i iy If the approximate confidence interval for the difference between two proportions does not contain 0 this provides evidence that the two proportions are not equal. The data in the table shows the observed frequencies of two drink preferences for independent samples of people who live in Town A and Town B. Using the approximate 99% confidence interval for the difference of two proportions determine if there is evidence to conclude that drink preference is associated with the town where the person lives.
QUESTION 19 (4 marks) A firm aims to have 95% confidence in estimating the proportion of office workers who respond to an email in less than an hour to within + 0.05. A survey has never been undertaken before so no past data is available. The firm believes that if the proportion is 0.5 then this will result in the largest variability in the sample proportion. Based on this determine the sample size needed using the approximate value of z = 2 for the 95% confidence interval. Justify the choice of 0.5 for the proportion.
QUESTION 3 A random sample of people were surveyed about the most important factor when deciding where to shop. The results appear in the table. Quality of merchandise Shopping environment If the sample size was 1200 the approximate 95% confidence interval for the proportion of people who identified price as the most important factor is (A) (0.395 0.405) (B) (0.386 0.414) (C) (0.377 0.423) (D) (0.372 0.428)
QUESTION 8 In a survey 80 respondents exercised daily while 120 did not. When calculating the approximate 95% confidence interval for the proportion of people who exercise daily the margin of error 1s 0.4(1-0.4) (A) 1.96 ——— 200 0.4(1-0.4) (B) 0.95——— 200 0.67(1-0.67) C) 1.96 |——— © 120 0.67(1—0.67) (D) 0.95 |————= 120
QUESTION 14 (8 marks) Ravi randomly sampled 200 different pet owners in Brisbane and found that 50 celebrate their pet`s birthday. a) Determine an approximate 95% confidence interval for the proportion of Brisbane pet owners who celebrate their pet`s birthday. [2 marks] Two of Ravi`s friends also randomly sampled Brisbane pet owners. The results are shown in the table. Friend`s name | Number sampled | Number who celebrate their pet`s birthday Khadija suggested a more precise estimate for the proportion of Brisbane pet owners who celebrate their pet`s birthday could be obtained by combining their results. b) Using all available data determine an approximate 95% confidence interval for the proportion of Brisbane pet owners who celebrate their pet`s birthday. [2 marks] c) Use the results from Questions 14a) and 14b) to evaluate the reasonableness of Khadija`s suggestion. [2 marks] The proportion of all Brisbane pet owners who celebrate their pet`s birthday is 0.24. d) Using the normal approximation determine the probability that in a randomly selected sample of size 200 more than 30% of pet owners celebrate their pet`s birthday. [2 marks]
QUESTION 10 If the sample size is decreased but the sample proportion and the confidence level remain the same the width of the confidence interval (A) will increase. (B) will decrease. (C) remains unchanged. (D) may increase or decrease.
QUESTION 10 A survey found that 142 out of 200 people aged 30 to 39 have some form of tertiary qualification. The approximate 95% confidence interval for the proportion of people aged 30 to 39 who have some form of tertiary qualification for this survey is (A) (0.62 0.80) (B) (0.63 0.79) (C) (0.65 0.77) (D) (0.66 0.76)
QUESTION 15 (8 marks) Suppose the proportion of Australians who supported the removal of single-use plastic bags from supermarkets is 64%. a) Using the normal approximation determine the probability that in a randomly selected sample of size 100 more than 70% of those surveyed supported the removal of the single-use plastic bags. [2 marks] b) Determine the size of the sample required for the survey to achieve a margin of error of 4% 1in an approximate 95% confidence interval for this proportion. [2 marks] c) Identify the effect that halving the margin of error has on the sample size obtained in 15b). [2 marks] d) Determine the probability that in a randomly selected sample of size 25 the sample proportion is equal to the population proportion. [2 marks]
QUESTION 8 A sample of size n was used to estimate a population proportion. An approximate margin of error of 3% was calculated using z = 1.96. Given the sample proportion was 0.6 determine n. (is6) (A) n= sb2es 0.24 008) 1.96 (oe) 1.96 C) na woe ) n= Ty wo) na 24 0.03 J 1.96
QUESTION 7 The distribution of a certain sample proportion has a mean of 0.70 and a standard deviation of 0.02. Determine the sample size. (A) 525 (B) 750 (C) 1750 (D) 2500
QUESTION 11 (4 marks) A researcher found that 17 out of 50 randomly selected people had used public transport in the past week. a) Determine the sample proportion of people who had used public transport in the past week. [1 mark] b) Determine an approximate 95% confidence interval for the proportion of people who had used public transport in the past week. [2 marks] c) Someone claims that: 50% of people use public transport each week. Use your answer from Question 11b) to explain whether the data can or cannot support this claim. [1 mark]
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