A random sample of 30 houses was selected to study the electricity consumption of a household during summers. The data on the electricity consumption (in kWh) for one month during summer are given in the following table <img src='./qimages/10343-1a.jpg'> Construct class-intervals of suitable width and continuous frequency distribution.
Draw the histogram.

(iii) Construct cumulative frequency distributions and ogives of "less than" as well as "more than" types. The local pizza restaurant advertises that they deliver pizza faster than the standard brand. In order to determine whether this advertisement is valid, some students decided to order 10 pizzas from the local pizza restaurant and 9 pizzas from the branch of standard brand at different times and recorded the delivery times (in minutes). The data are given in the following table: <img src='./qimages/10343-1b.jpg'>

Formulate the null and alternative hypotheses. Is variance of delivery time of the local pizza restaurant less than that of the standard brand at level of significance?

2.(a) Suppose that a fast-food chain wants to evaluate the service of eight restaurants. The Customer Service Director hires seven evaluators to act as raters. To reduce the effect of variability from rater to rater you use a randomised block design, with raters serving as the block. The eight restaurants are the groups of interest.

The seven raters evaluate the service of each of the eight restaurants in a random order. A rating scale from 0 to 100 (high) is used. The following table summarises the results <img src='./qimages/10343-2a.jpg'>

The effect of evaluation of each rater is normally distributed with approximately equal variances. Analyse the design at level of significance. Are average services of the eight restaurants significantly different If the difference between the average services of restaurants are significant, do the pair-wise comparison between them.

(ii) Find out which restaurant is most consistent as far as service is concerned.

3.(a) The following data represents the calories and fat (in grams) in 7 different types of cold coffee
<img src='./qimages/10343-3a.jpg'>

Draw the Box plots separately for calories and fat data.

(b) Nine contestants were rated by two experts in a cooking show for coffee making. A rating on a 7-point scale extremely unpleasant, 7 extremely pleasing) is given for each of the following five characteristics taste, aroma, richness, presentation and acidity. The following data displays the summated ratings accumulated over all five characteristics <img src='./qimages/10343-3b.jpg'>

Compute the rank correlation coefficient.