MATH-104, Statistics past quiz solution of first year, Lancaster University

In this pdf, I will be providing the handwritten solutions to past Quiz questions of MATH-104, First year, Lancaster University.

It includes the following questions.

QZ 19.7. Identify the critical t: An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the degrees of freedom and the critical t value (t⋆) for the given sample size and confidence level.

(a) n = 6, CL = 90%

(b) n = 21, CL = 99.9%

(c) n = 29, CL = 95%

(d) n = 12, CL = 99%

QZ 19.8 Young House Buying About 77% of young adults think they can buy a house by the time they are 30. Determine if the following statements are true or false, and explain your reasoning.

(a) The distribution of sample proportions of young adults who think they can buy a house by the time they are 30, in random samples of size 40 is approximately normal since n ≥ 30.

(b) The distribution of sample proportions of young adults who think they can buy a house by the time they are 30, in samples of size 20 is left-skewed.

(c) A random sample of 60 young adults where 85% think they can buy a house by the time they are 30, would be considered unusual when performing a two-sided hypothesis test at the 5% significance level.

(d) A random sample of 180 young adults where 85% think they can buy a house by the time they are 30, would be considered unusual when performing a two-sided hypothesis test at the 1% significance level.

(e) The standard error would be reduced by one-half if we increased the sample size from 60 to 120.

QZ 19.9 Elderly drivers: In January 2018, YouGov published a report stating that 66% of 1,018 adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age. Determine the margin of error for the 66% point estimate using a 95% confidence level. Give your answer to the nearest percent.