The management of a supermarket wanted to investigate whether the male customers spend less money on average than female customers. A sample of 22 male customers who shopped at this supermarket showed that they spent an average of $73 with a standard deviation of $17.50. Another sample of 20 female customers who shopped at the same supermarket showed that they spent an average of $87 with a standard deviation of $14.40. Assume that the amounts spent at this supermarket by all male and female customers are normally distributed with unequal and unknown population standard deviations.

a.) Construct a 90% confidence interval for the difference between the mean amounts spent by all male and all female customers at this supermarket.

b.) Using the 2.5% significance level, can you conclude that the mean amount spent by all male customers at this supermarket is less than that by all female customers?

c) Interpret the conclusion obtained in part b.

As part of a study designed to compare hybrid and similarly equipped conventional vehicles, Consumer Reports tested a variety of classes of hybrid and all-gas model cars and sport utility vehicles (SUVs). The following data show the miles-per-gallon rating Consumer Reports obtained for two hybrid small cars, two hybrid midsize cars, two hybrid small SUVs, and two hybrid midsize SUVs; also shown are the miles per gallon obtained for eight similarly equipped conventional models.

At the α = 0.05 level of significance, test for significant effects due to class, type, and interaction.

Find the value of the test statistic for class. (Round your answer to two decimal places.)

Find the p-value for class. (Round your answer to three decimal places.)

p-value =  

Find the value of the test statistic for type. (Round your answer to two decimal places.)

Find the p-value for type. (Round your answer to three decimal places.)

p-value =

Find the value of the test statistic for interaction between class and type. (Round your answer to two decimal places.)

Find the p-value for interaction between class and type. (Round your answer to three decimal places.)

p-value =

1.

A company's articles can contain provisions that cannot be altered

True

False

2.

In relation to a company's contractual capacity, the ultra vires doctrine has been abolished.

True

False

3.

Breach of any term in the statutory contract will allow either the company or a member to sue for breach of contract.

True

False

4.

Under the Companies Act 2006, you find the objects of a company set out in the Memorandum of Association.

True

False

5.

Companies incorporated under the Companies Act 2006 are not required to have a memorandum of association.

True

False

Internet service: An Internet service provider sampled 530 customers, and finds that 70 of them experienced an interruption in high-speed service during the previous month.

(b) Construct a 90% confidence interval for the proportion of all customers who experienced an interruption. Round the answers to at least three decimal places.

The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data311.dat gives the scores of 60 students who did this. How can we relate the two tests? (a) Plot the data with SAT on the x axis and ACT on the y axis. Describe the overall pattern and any unusual observations. (b) Find the least-squares regression line and draw it on your plot. Give the results of the significance test for the slope. (Round your regression slope and intercept to three decimal places, your test statistic to two decimal places, and your P-value to four decimal places.) ACT = + (SAT) t = P = (c) What is the correlation between the two tests? (Round your answer to three decimal places.)

obs     sat     act
1       1031    23
2       801     17
3       663     12
4       1096    27
5       693     17
6       906     22
7       708     17
8       1180    26
9       914     19
10      1099    25
11      775     20
12      1194    27
13      1009    21
14      899     22
15      833     18
16      1087    22
17      802     18
18      901     18
19      877     21
20      1049    20
21      868     17
22      792     17
23      1008    17
24      1167    25
25      554     10
26      1045    20
27      1206    28
28      875     22
29      798     19
30      1060    21
31      1124    26
32      1176    25
33      1068    23
34      732     12
35      741     14
36      969     22
37      593     12
38      613     19
39      619     14
40      1122    24
41      911     18
42      787     16
43      1033    26
44      781     14
45      941     26
46      989     24
47      756     15
48      1043    24
49      647     10
50      817     17
51      357     9
52      1157    27
53      1115    25
54      904     19
55      1094    27
56      837     19
57      573     12
58      749     18
59      1203    25
60      895     23

The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data5.dat gives the scores of 60 students who did this. How can we relate the two tests?

(a) Plot the data with SAT on the x axis and ACT on the y axis. Describe the overall pattern and any unusual observations.

(b) Find the least-squares regression line and draw it on your plot. Give the results of the significance test for the slope. (Round your regression slope and intercept to three decimal places, your test statistic to two decimal places, and your P-value to four decimal places.)

(c) What is the correlation between the two tests? (Round your answer to three decimal places.)

obs     sat     act
1       950     17
2       719     19
3       648     17
4       905     22
5       1263    29
6       995     25
7       1184    25
8       672     13
9       882     17
10      1082    21
11      875     17
12      951     20
13      1045    22
14      679     19
15      794     18
16      722     16
17      1227    28
18      746     14
19      1145    27
20      716     19
21      1208    28
22      950     21
23      890     23
24      761     17
25      969     17
26      647     11
27      857     21
28      991     21
29      798     17
30      666     14
31      761     19
32      660     20
33      631     16
34      1121    26
35      978     26
36      883     18
37      807     18
38      895     19
39      1184    23
40      869     17
41      582     14
42      1070    20
43      642     16
44      937     23
45      1086    27
46      1013    26
47      713     19
48      1144    25
49      990     24
50      878     16
51      870     26
52      1090    27
53      1095    26
54      781     19
55      1046    21
56      675     13
57      1257    25
58      1099    27
59      620     10
60      714     13

From the following balance sheet and additional information given, prepare cash flow statement.

Balance Sheet as on March 31, 2005 and 2006

Additional Information:

(a) Investments costing Rs.16,000 were sold during the year for Rs.17,000 (b) Provision for tax made out of profit was Rs.18,000 for the year (c) During the year, a part of the fixed assets costing Rs.20,000 was sold for Rs.24,000 and the

profit was included in Profit and Loss account (d) Dividends paid amounted to Rs.80,000