Response to the following questions:
Question 1
During 2002 the number of beds required per day at St Hallam's hospital was normally distributed with a mean of 1800 and a standard deviation of 190. During the first 50 days of 2003 the average daily requirement for beds was 1830. A senior hospital manager claims that this gives evidence that the requirements for beds has changed since 2001. Do you agree?
Question 2
The following data were obtained in an experiment to estimate a possible relation between the number of showings in one week of a TV commercial in typical sales territories and the sales (in thousands of units) in that territory of the advertised article.
|
Territory
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Showings
|
3
|
1
|
4
|
0
|
2
|
4
|
0
|
3
|
1
|
2
|
|
Sales
|
2.6
|
1.2
|
3
|
1
|
2
|
3.6
|
0.5
|
3.2
|
1.8
|
2.5
|
(i) Show that the data is significantly correlated.
(ii) Construct a scatter pot of the data.
(iii) Obtain a linear regression model for sales against number of showings per week.
(iv) What will be the estimated sales if there are 7 showings in a week? And for 20 showings?