PART 1

Continental tire is used for F-35 fighter jets in USA. Before every take off, the tire pressure and quality of

the tire is being measured. After allocating all the data, it's been found that Continental tires have an

average life span of 8000 hours in normal weather condition. However, in desert the average life span of

the tire becomes as low as 5000 hours. Suppose, the continental tire's average life span is what it gets

during normal weather condition and has a standard deviation of 400 hours. Find the probability that the

mean life of a random sample of 25 such tires is -

a) less than 7890 hours

b) between 7850 and 7910 hours

c) within 130 hours of the population mean

d) less than the population mean by 150 hours or more

Question 2:

Two thousand randomly selected adults were asked if they are in favor of or against cloning. The

following table gives the responses.

In Favor Against No Option

Male 395 405 100

Female 300 680 120

If one person is selected at random from these 2000 adults, find the probability that this person is-

a) in favor of cloning

b) against cloning

c) in favor of cloning given the person is a female

d) a male given the person has no opinion

e) Are the events "female" and "no opinion" independent? Why or why not?

Question 3:

A random sample of 8 observations taken from a population that is normally distributed produced a

sample mean of 44.98 and a standard deviation of 6.77. Find the critical and observed values of t and the

ranges for the p-value for each of the following tests of hypotheses, using = .05.

a. H0: = 50 versus H1: 50

b. H0: = 50 versus H1:

Question 4: 12 Marks

Heinz, a manufacturer of ketchup, uses a particular machine to dispense 16 ounces of its ketchup into

containers. From many years of experience with the particular dispensing machine, Heinz knows the

amount of product in each container follows a normal distribution with a mean of 16 ounces and a

standard deviation of 0.15 ounce. A sample of 50 containers filled last hour revealed the mean amount

per container was 16.017 ounces. Does this evidence suggest that the mean amount dispensed is different

from 16 ounces? Use the .05 significance level.

(a) State the null hypothesis and the alternate hypothesis.

(b) What is the probability of a Type I error?

(c) Give the formula for the test statistic.

(d) State the decision rule.

(e) Determine the value of the test statistic.

(f) What is your decision regarding the null hypothesis?

(g) Interpret, in a single sentence, the result of the statistical test.

\fLet X1 and X2 be independent random variables having the standard normal distribution. Obtain the joint Lebesgue density of (Y1, Yz), where Yi = VX?+ X} and Y2 = X1/X2. Are Y1 and Y2 independent? Note. For this type of problem, we may apply the following result. Let X be a random k-vector with a Lebesgue density fx and let Y = g(X), where g is a Borel function from (R*, B* ) to (R*, B*). Let A1, . .., Am, be disjoint sets in B* such that R* - (Aj U . . . U Am,) has Lebesgue measure 0 and g on A; is one-to-one with a nonvanishing Jacobian, i.e., the determinant Det(Og(x)/Or) # 0 on Aj, j =1. .... m. Then Y has the following Lebesgue density: fy (x) = >Det (Oh, (x)/ar) | fx (h,(r)). j=1 where h, is the inverse function of g on A;, j = 1, ..., m.3. A US company pays interest for $30,000 matured on its bonds held by a German investor. The payment is in Dollars. The German investor sells the Dollars to the European Central Bank (official institution). How do you record this transaction in the US Balance of Payments? Current Account $30,000 Financial Account (Non-official) (a) Financial Account (Official) $30.000 Current Account Financial Account (Non-official) (b) $30.000 $30,000 Financial Account (Official) Current Account $30,000 Financial Account (Non-official) (c) Financial Account (Official) $30,000 Current Account Financial Account (Non-official) (d) $30.000 Financial Account (Official) $30,000 3Select the correct statement regarding managerial and financial accounting. Users of managerial accounting information desire more detailed accounting reports than do users of financial accounting information. Both managerial and financial accounting use economic and physical data in addition to financial data. Financial accounting is less regulated than managerial accounting. Timeliness is more important in financial accounting than in managerial accounting 3. Assume that the US resident uses his 112,000 JPY to purchase a camera from a store in Japan and then brings it back to the US. The transaction can be recorded by noting the foowing (for the US): (a) +$1.000 Financial account, $1.000 Capital account. (b) +$1.000 Financial account, $1.000 Current account. (c) +$1.000 Current account, $1.000 Financial account. ) l (d +$1.000 Financial account, $1.000 Financial account. [e +$1.000 Capital account, ~$1.000 Financial account