8 MULTIPLE CHOICE QUESITONS 1. 2. 3. 4. 5. 6. 8.

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8 MULTIPLE CHOICE QUESITONS
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A researcher is interested to know if smoking and heart disease are associated in the population of New Zealand. The researcher takes a census of the population in New Zealand with a 100% response rate. The researcher conducts a chi-squared test on the census data at 5% significance level and obtains a p- value of 0.001. Which of the following is a valid conclusion? Since p-value is less than 0.05, the null hypothesis is rejected at the 5% significance level, and the researcher concludes that smoking and heart disease are not associated in the population, None of the other options are valid conclusions. Since p-value is less than 0.0s, the null hypothesis is not rejected at the 5% significance level, and the researcher concludes that smoking and heart disease are associated in the population Since p-value is less than 0.05, the null hypothesis is rejected at the 5% significance level, and the researcher concludes that smoking and heart disease are associated in the population. Since p value is less than 0.05, the null hypothesis is not rejected at the 5% significance level, and the researcher concludes that smoking and heart disease are not associated in the population

Suppose that there are 76 pairs of siblings living in a particular block, where the older sibling is always heavier than the younger sibling. Consider a scatter plot using the younger sibling's weight to predict the older sibling's weight, where each point in the scatter plot represents a set of two siblings in the block. Which of the following statements must be true? (1) There is a positive association between the older and younger sibling's weights. (II) All the points lie above the line y=x in the scatter plot. (only. Neither (1) nor (11). Both (I) and (m). (lt) only

Suppose we want to test if a coin is biased towards heads. We decide to toss the coin 10 times and record the number of heads. We shall assume the independence of coin tosses, so that the 10 tosses constitute a probability experiment. Let X denote the number of heads occurring in 10 independent tosses of the coin. We will carry out a hypothesis test with X as the test statistic. Let H be the event that the coin lands on head, in a single toss. Set our hypothesis to be • Ho: “P(H) = 0.5”, • H1 :"P(H) > 0.5”. = Suppose in our execution of the 10 tosses, we observe 4 heads. This means X = 4 is the test result we observe. Recall the definition of p-value to be the probability of obtaining a test result at least as extreme as the one observed, assuming the null hypothesis is true.' What is the range of test results "at least as extreme as the one observed", in this scenario? (1 mark) 4< X < 10. 5 < X < 10. 0 < X<5. 0 < X < 4.

Module XYZ's midterm results for year 2050 Semester 1 are shown in the box plot below. There were 50 students who took the test, and the test scores are out of 100. No outliers were removed. Midterm Results 100 9100 CE 90 8 Soora 70 70 25 8 cs 206051 Sem 1 Which of the following can be derived from the box plot? Select all that apply. (1 mark) The standard deviation is 14. The interquartile range is 40. There is at least one outlier. The range is 40.

A study was conducted on 1000 students in a secondary school on 11th January 2021. On that day, of these 1000 students, 80% of the students took the MRT (mass rapid transit) to school. Among those students that took the MRT to school, 10% were late for school. Among those students who did not take the MRT to school, 20% were late for school. Among those students who were late for school, a student was randomly chosen, with every student having the same chance of being selected. What is the probability (correct to 1 decimal place) that the chosen student did not take the MRT? 20.0% 33.3% 10.0% 30.096

the gradient of the If an outlier is removed from a data set of two variables, the gradient of the new regression line without the outlier can be original regression line with the outlier. Which of the following can be used to fill in the blank? Select all that apply. (1 mark) greater than smaller than the same as

A nutritionist wants to estimate the average mass of a particular tortilla chip brand, Naritos. He decides to collect a sample of 100 packets of Naritos chips, using the method described as follows: He went down to the nearest factory that produces Naritos chips and measured the average mass of the first 100 packets of Naritos chips produced on that day. You can assume the mass of the packaging is negligible. The sample he collected had a sample mean of 700 grams, and gave a 95% confidence interval for the population mean as [676.3, 723.7]. Which of the following statements must be true? (1) If we collect 100 samples of 100 packets of Naritos chips using the same sampling method, about 95 of the samples will have confidence interval containing the population average mass of Naritos chips. (II) We can conclude that there is a 95% chance that the population average mass of Naritos chips lies within [676.3, 723.7]. (1 mark) (II) only. (1) only. Neither (1) nor (II). Both (I) and (II).

The scatter plot below shows the relationship between height and shoulder girth (circumference of shoulders measured over deltoid muscles). 200 0 180 Height (cm) 160 170 eo హలం లో 0 B O Oo 0 0 150 90 100 120 130 110 Shoulder Girth (cm) The equation of the regression line for height vs shoulder girth is given by y = 0.6x + 106, where y refers to the height and x refers to shoulder girth. Which of the following statements is/are correct? Select all that apply. (1 mark) If the shoulder girth of all the individuals above are 2cm shorter, then the gradient of the regression line for height vs shoulder girth is 0.6. Using simple linear regression, when the shoulder girth is equal to 141cm, the predicted average height is 190.6cm. If we were to predict shoulder girth from height using simple linear regression, the gradient of the regression line is also positive. Using simple linear regression, when the height of the individual is 170cm, the predicted average shoulder girth is 106.67cm.