1) British statistician and biologist introduced a data set which consists of 50 samples from Iris setosa. The length of sepals was measured from each sample in centimetres. A long-term study says that the average length of sepals of Iris setosa is 5.5 centimetres. The data set is available below.

a) What conditions are needed to proceed with inference using this data? Perform a check to show that the conditions are valid.

b) Determine if the data provides evidence that the mean sepal length of Iris setosa is different to the traditional 5.5 cm, by

1. constructing a 95% confidence interval, and

2. conducting a suitable test at the 5% significance level.

c) Is the conclusion from the confidence interval calculation above the same as the conclusion of the test above? Explain why or why not.

Sepal.Length

Iris setosa

5.1

4.9

4.7

4.6

5

5.4

4.6

5

4.4

4.9

5.4

4.8

4.8

4.3

5.8

5.7

5.4

5.1

5.7

5.1

5.4

5.1

4.6

5.1

4.8

5

5

5.2

5.2

4.7

4.8

5.4

5.2

5.5

4.9

5

5.5

4.9

4.4

5.1

5

4.5

4.4

5

5.1

4.8

5.1

4.6

5.3

5

2) A survey in a large unit for first-year college students asked, "About how many hours do you exercise during a week?" The mean response of the 600 students was 2.2 hours. Suppose that the standard deviation of exercise time is = 1.3 hours in the population of all first-year students at this college.

a) What is the point estimate of the mean time in exercising for a week in the population of all firstyear students at this college? b) Check conditions for a confidence interval for the mean exercise time.

c) Use the survey result to construct a 95% confidence interval for the mean exercise time. Interpret the confidence interval.

d) The mean response was mistakenly recorded as 22 hours. Using this value, construct a 95% confidence interval for the mean exercise time, and state the effect of this mistake in the confidence interval.