MATH-104, Statistics, First year Lancaster University, past assignment solution

In this pdf, I will be providing the solution of past assignment of Statistics subject, Bachelor Program, of Lancaster University. It includes the solutions to the following questions.

Coursework Questions

CW 18.8. Online communication: A study suggests that the average university student spends 2.5 hours per week communicating with others online. You believe that this is an underestimate and decide to collect your own sample for a hypothesis test. You randomly sample 70 students from your accommodation and find that on average they spent 3.75 hours a week communicating with others online. A friend of yours, who offers to help you with the hypothesis test, comes up with the following set of hypotheses. Indicate any errors you see.

H0: ¯x < 2.5 hours

HA: ¯x > 3.75 hours

CW 18.9. Speed reading: A company offering online speedreading courses claims that students who take their courses show a 5 times (500%) increase in the number of words they can read in a minute without losing comprehension. A random sample of 100 students yielded an average increase of 412% with a standard deviation of 218%. We want to assess the companies’ claim.

(a) Perform a hypothesis test evaluating if the company’s claim is reasonable. Make sure to interpret your response in context of the hypothesis test and the data. Use α = 0.025. (Note that you can assume that the conditions for inference are satisfied from last week’s coursework.)

(b) Do your results from the hypothesis test and the confidence interval (last week’s homework) agree? Explain.

CW 18.10. Weight gain during pregnancy: In 2004, the state of North Carolina released to the public a large data set containing information on births recorded in this state. This data set has been of interest to medical researchers who are studying the relationship between habits and practices of expectant mothers and the birth of their children. The following histograms show the distributions of weight gain during pregnancy by 866 younger mums (less than 35 years old) and 135 mature mums (35 years old and over) who have been randomly sampled from this large data set. The average weight gain of younger mums is 31.56 pounds, with a standard deviation of 14.75 pounds, and the average weight gain of mature mums is 28.77 pounds, with a standard deviation of 13.58 pounds.

(a) Calculate a 95% confidence interval for the difference between the average

weight gain of younger and mature mums.

(b) Comment on whether or not this interval provides strong evidence that there is a significant difference between the two population means.

(Histograms are given here)

CW 18.11 Find the sample mean: You are given the following hypotheses: H0: µ = 34, HA: µ > 34. We know that the sample standard deviation is 10 and the sample size is 65. For what sample mean would the p-value be equal to 0.05? Assume that all conditions necessary for inference are satisfied.