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1a) Define the term confidence interval, and relate it to the term confidence level
b) Name two (2) factors that will affect the width of a confidence interval.
c) A survey was conducted to record the heights of students in a different university. Based on a sample of 89 male students, the mean height was found to be 172 cm, with a standard deviation of 22.5 cm. As for the sample of 107 female students, the mean height was found to be 161 cm, with a standard deviation of 27.3 cm. The two populations both follow the normal distribution.
ci) Estimate the 95% confidence interval for the population mean, for male and female students respectively.
cii) Given that the population standard deviation for male students is 23.9 cm and for female students 27.8 cm, find the difference between the two population means at 99% confidence interval. Based on the confidence interval obtained, explain if the difference between the two population means is significant.
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