A fruit juice producer conducted a study at a large supermarket to determine the possible influence of different package designs on the sales volume of their one-liter cartons of pure apple juice. The apple juice was sold in pyramid-shaped cartons for the first eight weeks, after which the same product packaged in barrel-shaped cartons was sold for a further eight weeks. Weekly sales (in cases) were recorded over each eightweek period. Pyramid 27 16 25 32 20 22 26 22 Barrel 25 28 34 28 22 35 18 29 Assume weekly sales are normally distributed for each carton design and that population variances are equal. If the marketer’s decision is to choose the package design that is likely to lead to large national sales, on average, should they use the barrel-shaped carton design? Conduct a hypothesis test at the 1% level of significance to determine if the mean weekly sales of pure apple juice in the barrel-shaped carton design are greater than the mean weekly sales in the pyramid-shaped carton. Use critical value approach.
1. A fruit juice producer conducted a study at a large supermarket to determine the
possible influence of different package designs on the sales volume of their one-liter
cartons of pure apple juice. The apple juice was sold in pyramid-shaped cartons for the
first eight weeks, after which the same product packaged in barrel-shaped cartons was
sold for a further eight weeks. Weekly sales (in cases) were recorded over each eightweek period.
Pyramid 27 16 25 32 20 22 26 22
Barrel 25 28 34 28 22 35 18 29
Assume weekly sales are
population variances are equal. If the marketer’s decision is to choose the package
design that is likely to lead to large national sales, on average, should they use the
barrel-shaped carton design? Conduct a hypothesis test at the 1% level of significance
to determine if the
design are greater than the mean weekly sales in the pyramid-shaped carton. Use critical
value approach.
2. According to the records of the National Safety Council, accidental deaths in the South
Africa during 2010 had the following distribution according to the principal types of
accidents.
Motor
Vehicle
Falls Drowning Fire Poison Other
45% 15% 4% 3% 16% 17%
Suppose that an accidental death data set from a particular geographical region yielded the
following frequency distribution for the principal types of accidents:
Motor Vehicle Falls Drowning Fire Poison Other
442 161 42 33 162 150
Do these data show a significantly different pattern in the distribution of accidental deaths in
the particular region compared to the pattern in the entire South Africa? Use a 1% significance
level.
3. An urban community would like to show that the incidence of breast cancer is higher
in their area than in a nearby rural area. If it is found that 20 of 200 adult women in the
urban community have breast cancer and 10 of 150 adult women in the rural community
have breast cancer.
a) Can we conclude at the 0.05 level of significance that breast cancer is more
prevalent in the urban community? Make use of a p-value approach.
b) What is the 99% confidence interval for the difference between the two
population proportions?
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