1. Since careful records have begun being kept in January, Eric’s small business has delivered the following quantities of flowers throughout the town.

January Feb March April May June July August

Small Bouquets 85 34 26 24 43 29 30 19

Large Bouquets 23 64 27 18 33 23 20 13

Assuming the data is normally distributed, construct two separate 90% confidence intervals, one for the number of deliveries of small bouquets in September and one for the large bouquets in September.

2. Consider the following data values of variables x and y.

X- 5 4 3 6 9 8 10
Y- 7 8 10 5 2 3 1

Construct a scatter diagram of the data points and plot the least squares regression line on it. Find the least squares regression line.

3. A quality control experiment is to be done on a machine that fills tubes with tooth paste. Its specifications require that it fill tubes with 4.7 oz. A random sample of 40 tubes filled by the machine is taken and each tube is weighed. The resulting data are below, with the weight of the tube already having been subtracted from each. Perform a hypothesis test at the 90% confidence level to determine is the machine is performing according to specifications.

4.66 4.61 4.71 4.63 4.70 4.62 4.63 4.61 4.70 4.56
4.60 4.66 4.68 4.57 4.67 4.72 4.67 4.64 4.66 4.75
4.69 4.64 4.67 4.65 4.69 4.65 4.75 4.53 4.57 4.74
4.68 4.67 4.66 4.68 4.64 4.65 4.64 4.80 4.71 4.69

PLEASE SHOW ALL WORK