SIT191 - Introduction to Statistics and Data Analysis - Statistics Assignment Help

Assignment Task

Question 1 Heights for 8 year old girls are normally distributed with a mean of 127 cm and a standard deviation of 3 cm.

a) Sketch the normal model for the girls’ heights.

b) In what interval would you expect the central 95% of heights to lie?

c) What percentage of the girls are taller than 131 cm?

d) Below what height are the shortest 25% of girls?

e) If 15 girls are randomly selected, find the probability that their average height is greater than 129 cm.

Question 2 The recommended amount of sleep for young adults is 7 to 9 hours per night. A random sample of 30 university students reported a mean nightly sleep time of 6.53 hours and standard deviation of 1.12 hours.

a) Using a suitable hypothesis test procedure, test the hypothesis that university students are not meeting the minimum sleep requirement. Use α = 0.05 and include all the steps.

b) Calculate a 90% confidence interval for the true mean amount of sleep, and interpret the interval.

c) Comment on the hypothesis test conclusion from part a) in relation to the confidence interval found in part b).

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