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A seller claimed that her lip tint has a mean organic content 90%
A researcher wants to understand how an annual mortgage payment (in Ringgit) depends on
income level and zonal location allowing for interaction. The data are shown below.
a.Specify the null and alternative hypotheses to test whether there is interaction between
income and zonal location. (2 Marks)
b. Determine the total sum of square, sum of square for income (factor A), sum of square
for zonal location (Factor B), sum of square for the interaction between income and zonal
location, and error sum of square. (10 Marks)
c. Determine the mean square for income (factor A), mean square for zonal location (Factor
B), mean square for the interaction between income and zonal location, and mean square
error. (4 Marks)
d. Determine the F-Statistics and P-Value for income, zonal location and interaction between
income and zonal location. (6 Marks)
e. At the 5% significance level, can you conclude there is interaction between income and
zonal location?
If 5 samples from 5 populations are given, then what is the probability of getting at least one Type 1 error at 90% confidence interval?
If 5 samples from 5 populations are given, then what is the probability of getting no Type 1 error?
Mr. Ali runs a gift shop in the Defense area, Karachi. He advertises weekly in the local newspapers and is considering increasing his advertising budget. Before doing so, he decides to evaluate the past effectiveness of these advertisements. Five weeks are sampled, and the advertising expenses (in PKR) and sales volume for each is shown in the Table 2. Develop a regression equation that would help Mr. Ali evaluate his advertising. FInd slope of this regression equaiton.
S.No.
Sales (PKR 100)
Advertising (PKR 100)
1.00
6.00
4.10
2.00
8.00
6.72
3.00
6.00
5.05
4.00
10.00
7.26
5.00
6.00
2.69
- Pepsi Co. Pvt Ltd is planning to produce a new energy drink. For this purpose, a pilot study was conducted using four different energy drinks formula. They were tested on 3 different sets of people and the reactions in energy level of the people were measured forming four groups. Using the data (measured energy level values) provided below, test whether there is difference in the four energy drinks. Perform this by finding F ratio. What is critical F value, i.e. Fc at 95% confidence interval?. The data is as shown in Table 1.
Formula 1
Formula 2
Formula 3
Formula 4
64
46
43
38
55
42
32
45
80
42
45
37
Mr. Ali runs a gift shop in the Defense area, Karachi. He advertises weekly in the local newspapers and is considering increasing his advertising budget. Before doing so, he decides to evaluate the past effectiveness of these advertisements. Five weeks are sampled, and the advertising expenses (in PKR) and sales volume for each is shown in the Table 2. Develop a regression equation that would help Mr. Ali evaluate his advertising. FInd constant of this regression equaiton.
S.No.
Sales (PKR 100)
Advertising (PKR 100)
1.00
6.00
4.10
2.00
8.00
6.72
3.00
6.00
5.05
4.00
10.00
7.26
5.00
6.00
2.69
Show that the adjusted sample variance is a consistent estimator of the true variance
Mr. Ali runs a gift shop in the Defense area, Karachi. He advertises weekly in the local newspapers and is considering increasing his advertising budget. Before doing so, he decides to evaluate the past effectiveness of these advertisements. Five weeks are sampled, and the advertising expenses (in PKR) and sales volume for each is shown in the Table 2. What is correlation coefficeint value?
S.No.
Sales (PKR 100)
Advertising (PKR 100)
1.00
6.00
4.10
2.00
8.00
6.72
3.00
6.00
5.05
4.00
10.00
7.26
5.00
6.00
2.69
A shopper goes to the grocery store and purchases a bag of 10 apples. Based on previous
experience, he knows that 5% of the apples of this brand will be bruised and inedible. Assume
that the apples are randomly assigned to the bag.
(i) State the mean and variance of the distribution of the number of bad apples in the bag.
(2)
(ii) What is the probability that in his bag he has either no bad apple or only one bad apple?
(4)
(iii) What is the probability that in his bag he has at least seven good apples?
