A10. The following two sample t-test compares the weekly hours spent studying between independent samples of students wh

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A10. The following two sample t-test compares the weekly hours spent studying between independent samples of students whose social media of choice is snapchat or instagram. t.test(social_data$studying - social_data%social, conf.level = 0.95, alternative = "two-sided") Welch Two Sample t-test a data: social_data$studying by social data$social t = 3.1884, df = 14.063, p-value = 0.006539 alternative hypothesis: true difference in means is not equal to O 95 percent confidence interval: 1.740907 8.887664 sample estimates: mean in group instagram mean in group snapchat 9.714286 4.400000 Which one of the following statements is correct? a. The confidence interval does not contain 0 which suggests there is a no difference in mean studying time between the groups. b. The confidence interval contains 0 which suggests there is a no difference in mean studying time between the groups. c. When testing at a = 0.05, the test statistic 3.1884 is not small, there is no evidence to suggest H. : 11 - 12 +0. d. When testing at a = 0.05, the p-value 0.006539 is small, there is no evidence to suggest H.: H1 - H270. e. When testing at a = 0.001, the p-value 0.006539 is small, there is evidence to suggest H:Hi-H2 +0. f. When testing at a = 0.01, the p-value 0.006539 is small, there is evidence to suggest HM-M20. [3 Marks) = .

38 A8. The School of Mathematics, Statistics and Applied Mathematics runs a maths drop in centre SUMS. SUMS wanted to test whether the service was being used equally by undergraduate students from 1st, 2nd, 3rd and 4th year. They observed the following data in a single day: First Second Third Fourth Total Students 32 12 18 100 To start their hypothesis test, they must set up their null and alternative hypotheses. Which of the following is correct? a. Ho: P = P2 = P3 = Pa; Hapi #p, for all i and b. H. : P1 = P2 = P3 =p4: H. : P1 > P2 > P3 > P4 c. Ho: P = 0.38.p2 = 0.32.P3 = 0.12, pe = 0.18; H, : At least one of the pi's is not equal to the assumed values d. H: P1 = P2 = P3 = P4; H. : P: + p, for some combination of i and i [3 Marks) : A9. Which of these is NOT an assumption required when performing a simple linear regression? a. A linear relationship between predictor X and response Y b. The residuals have a constant variance c. The residuals have mean 0 d. The residuals follow a Normal distribution e. The residuals are independent f. The sample size n must be bigger than 30 [3 Marks)

A6. A random sample of n=100 individuals from a population with unknown mean y is to = be used in testing the hypotheses H. : x = 7 versus H. : > 7 at significance level a =0.01. It is assumed the population standard deviation is known to have value o =2. The power function is a. Cannot determine the power function since the sample mean I has not been observed. b. P(Z > for > 7. d. P(Z > for p > 7. e. 1+P(Z < 6-4844) - P(Z < 7518+) for u +7. [3 Marks) 7.466–- for p > 7. c. P(Z > 0.2 7.392- 0.2 7.328- 0.2 0.2 0.2 A7. In a particular analysis, a 90% CI for a difference in population proportions contained zero. Without calculating anything, what can you say about the accompanying p-value for a test of no difference in population proportions? a. p<0.001 b. p > 0.1 c. p < 0.01 d. p<0.1 e. p < 0.05 [3 Marks)

A2. Which one of the following is the correct interpretation of the standard error of the estimate? a. The accuracy of a sample statistic for a sample of size n in estimating the population parameter. b. A measure of the variability in a sample of n observations of the random variable X. c. Error in calculation of the sample statistic. d. A measure of the variability in sample statistics for all possible samples of size n taken from a population of individuals. [3 Marks) X 7 0 < A3. Suppose that the random variable X for a certain population has a normal distribution with mean I and variance o?, X - Normal(u,02). Also, let X1, X2, X, be a random sample of size n > 1 from the population and let X-Xi Define a = P(|X – <:), = P(X-4<), and c = P(Z < 1) where Z Normal(0.1). What is the relationship between a, b and c? a. all three of the numbers a, b and c are equal b. a=b+c c. a=c+b d. b=ca e. all three of the numbers a, b and c are distinct. 3 Marks) A4. A random sample of size n = 6 is taken from a normal population. We find a 95% confidence interval for the mean of the population to be 5.4<x< 13.2. Which one of the following would result in an interval estimate that is more precise, i.e. narrower than that calculated above? a. Decreasing the confidence level. b. If the mean of the sample was equal to the population mean. c. Decreasing the significance level a d. Taking a sample that is smaller in size. e. If the population was more variable, i.e. larger o. [3 Marks)

Al. The boxplots below provide a summary of the observations of hours per week spent exercising recorded for a sample of data science, financial mathematics and mathematics students. ggplot (dat, aes (x = type, y = exercising, fill = type)) geom_boxplot() + labs(y="Weekly hours exercising (hours)") 25 Weekly hours exercising (hours) type Data Science Financial maths Maths 10 - 0- Data Science Maths Financial maths type Which one of the following statements is FALSE? a. The observed upper quartile for data science is lower than the observed lower quartile for financial maths. b. Each box represents the interquartile range, the range of values of the middle 50% of the data. c. Outliers are marked as values outside the range (Q1 -1.5(Q3-01), Q3+1.5(Q3-01)). d. The observed median for maths is greater than the observed median for financial maths. e. The financial maths data are positively skewed. [3 Marks)