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Assignment#2 ECON 2330 Winter 2021
1) A bank holds the mortgage on a motel which the motel owner says has an average daily revenue of at least $2048. In the event the average is not at least $2048, the bank will ask the motel owner for additional collateral for the loan as protection against loan default. A loan officer is aware that the daily average revenue is normally distributed and randomly selects 40 days during the last six months. The sample has a mean of $2003 and standard deviation of $144.00. (Assume a= 0.05).
a) Set up Ho and Ha. b) What is the value of the test statistic? c) Plot your test distribution and clearly identify the rejection and the p-value areas
(with two different colours). d) Is the bank loan financially sound (should the bank ask for additional collateral)?
2) It has been reported that the average visitor from Japan spent $3120 during a trip to the Canada, while the average for a visitor from the United Kingdom was $2654. Using the data provided below, use α=0.05 level, examine whether the sample mean for Japanese visitors is significantly higher than that for visitors from the United Kingdom. Show your steps how did you arrive at the p-value for the test and how do you interpret it.
Japan 2507 3145 4898 1852 3208 3545 2856 3908 3248 4520 3008 2845 4014 2251 5302 3303 2774 3013 3178 2204 2057 2107 2620 3480 3114 3377 3496 2932 2856 3008 2094
United Kingdom 3739 2397 2554 1266 2631 2036 1588 3490 2126 3006 2678 2664 3424 3609 3465 2390 3217 3018 1898 2428 2523 3415 1931 2810 2433 2577 3024 2495 3465 1909 2590 1891 2721 2828
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3) A battery manufacturer claims that their new “long-lasting” battery has an average life that is significantly longer than their competitor’s “regular” battery. Both types of batteries were tested and the number of hours each battery lasted is shown in the following table.
a) State the null and alternative hypothesis. b) Using = 0.05, state the decision rule in terms of the critical value. c) Using = 0.05, state your conclusions.
Now, assume that from the production perspective we are interested in testing if the reliability of the production of “long- lasting” battery is significantly better than the “regular” battery.
d) State the null and alternative hypothesis. e) Using = 0.01, state the decision rule in terms of the critical value. f) Using = 0.01, state your conclusions.
Long- Lasting Battery
Regular Battery
51 42 44 29 58 51 36 38 48 39 53 44 57 35 40 40 49 48 44 45 60 50
4) Suppose that in an attempt to target its clientele, managers of a local supermarket chain want to determine the difference between the proportion of morning shoppers who are men and the proportion of after–6 p.m-shoppers who are men. Over a period of two weeks, the chain's researchers conduct a systematic random sample survey of 400 morning shoppers, which reveals that 352 are women and 48 are men. During this same period, a systematic random sample of 480 after–6 p.m. shoppers reveals that 293 are women and 187 are men. Construct a 98.5% confidence interval to estimate the difference in the population proportions of men. Carefully interpret the outcomes.
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5) Twenty-five recorded food delivery times to the same points of delivery in the same city for two local delivery food companies have been provided below. Do the data indicate a difference in mean delivery times for the two companies? Use a 0.01 level of significance and you are only allowed to construct a confidence interval.
Company A Company B 11 9.7
13 5.4
14.3 19
18.5 15.8
30 9.3
13.5 29
16.5 5.8
22 14
16.4 2.5
20.5 12
10.5 15.3
16 14.1
12.6 12.3
11.5 10.6
8.5 11.4
14.3 21.8
15.1 13.4
11.8 6.4
16.2 5.3
11 9.6
12 14.5
19 5.2
11.5 6.6
14.5 8.7
27.5 29
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6) Social networking is becoming more and more popular around the world. Pew Research Center used a survey of adults in several countries to determine the percentage of adults who use social networking sites (USA Today, February 8, 2012). Assume that the results for surveys in Great Britain, Israel, Russia, and United States are as follows.
Great Britain Russia Israel
United States
Yes 344 265 301 500 No 456 235 399 500
a) Conduct a hypothesis test to determine whether the proportion of adults using social
networking sites is equal for all four countries. What is the p-value? Using a 0.05 level of significance, what is your conclusion?
b) What are the sample proportions for each of the four countries? Which country has the largest proportion of adults using social networking sites?
c) Using a 0.05 level of significance, conduct multiple pairwise comparison tests among the four countries. What is your conclusion?
7) The five most popular art museums in the world are Musée du Louvre, the Metropolitan
Museum of Art, British Museum, National Gallery, and Tate Modern (The Art Newspaper, April 2012). Which of these five museums would visitors most frequently rate as spectacular? Samples of recent visitors of each of these museums were taken, and the results of these samples follow.
Musée du
Louvre Metropolitan
Museum of Art British
Museum National Gallery
Tate Modern
Rated
Spectacular 113 94 96 78 88
Did Not Rate
Spectacular 37 46 64 42 22
a) Use the sample data to calculate the point estimate of the population proportion of visitors who rated each of these museums as spectacular.
b) Conduct a hypothesis test to determine if the population proportion of visitors who
rated the museum as spectacular is equal for these five museums. Using a .05 level of significance, what is the p-value and what is your conclusion?
8) A salesperson makes twenty calls per day. A sample of 150 days gives the following
frequencies of sales volumes.
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Records show sales are made to 16% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial probability distribution.
a) Compute the expected frequencies. Make sure you satisfied the technical requirement of a binomial distribution.
b) Use the goodness of fit test to determine whether the assumption of a binomial probability distribution should be rejected. Use a=0.05. Because no parameters of the binomial probability distribution were estimated from the sample data, the degrees of freedom are k − 1 when k is the number of categories.
c) Provide a plot of both the theoretical and observed distributions in one graph.
Number of Sales
Observed Frequency (days)
0 8 1 12 2 18 3 19 4 25 5 9 6 10 7 7 8 7 9 4 10 5 11 2 12 3 13 2 14 1 15 6 16 5 17 2 18 3 19 0 20 2