Question 3 [1 mark] During exploratory and formal analysis of this question, the following plots and numerical summary were produced. Histogram of Span-Height Probability Plot of Span-Height Normal - 951 0 AD Frequency 13: 15 SpanHeight Span-Haight Statistics Variable N Mean StDev Minimum Q1 Median Q3 Maximum IQR Skewness Span-Height 57 0.684 5.392 -12.000 -3.000 1.000 3.000 16.000 6.000 0.25 What conclusion should be drawn from these plots and the numerical summary? (a) The points lie close to the line of best fit, so we can assume a linear relationship between arm span and height. [b) Although there are two outliers on the Normal probability plot, the sample size is large enough to allow a valid t-test to be performed. (c) The variable is clearly bimodal, so a valid test cannot be performed on this variable. (d) There is not enough spread in the data to allow a valid test to be performed. (e) The histogram is right-skewed, contradicting the Normal probability plot. (f) None of the above statements is correct.Question 4 [1 mark] The researchers from Question 1 decided to use a t-test for their formal statistical analysis and obtained the following output. Descriptive Statistics Test N Mean StDev SE Mean 95% Cl for u Null hypothesis Ho: H = 0 57 0.684 5.392 0.714 (-0.747, 2.115) Alternative hypothesis Hu u # 0 H: population mean of Span-Height T-Value P-Value 0.96 0.342 In addition to performing the test, a confidence interval was calculated. Assuming that the chosen analysis method was valid, this interval may be interpreted as follows: (a) The true mean value of arm span minus height for adults is fixed but unknown and we are 95% confident that this fixed value is either greater than 2.115cm or less than -0.747cm. (b) The true mean value of arm span minus height for adults is fixed and is known to lie between approximately -0.747cm and 2.115cm. MAB141 Semester 2 2021 Stats Quiz 2 Page 2 of 6 (c) The true mean difference between arm span and height of adults varies and we are 95% confident that the mean arm span is between 0.747cm lower and 2.115cm higher than the mean height. (d) The true mean value of arm span minus height for adults is fixed but unknown and we are 95% confident that the interval from -0.747cm to 2.115cm includes this fixed value.Question 1 [1 mark] It is commonly believed that a person's arm span is equal to their height. To help test this claim, a sample of students from QUT was asked to record their arm span and height (both in cm). Assuming that this sample is representative of the general population of adults, what is the null hypothesis (Ho) for this test? (Note: in the following statements, "typical" refers to either the mean or the median value, depending on which test is used.) (a) The typical arm span is lower than the typical height for adults in this sample. (b) The typical arm span is lower than the typical height for adults in the population. (c) The typical arm span and typical height of adults in this sample are not equal. (d) The typical arm span and typical height of adults in the population are not equal. (e) The typical arm span is higher than the typical height for adults in this sample. (f) The typical arm span is higher than the typical height for adults in the population. (g) The typical arm span and typical height of adults in this sample are equal. (h) The typical arm span and typical height of adults in the population are equal