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1. The 95% confidence interval for the mean of a population is (49.2, 55.4). If a hypothesis

is run at 1% level of significance using Ho: u= 49 and Hi>49 would the null hypothesis

be rejected?

In order to answer the problem we need not solve entirely because insufficient data has

been given. Clearly, the null hypothesis is rejected because if we base only on the values

and the confidence limit given in solving

From this, a large deviation and leeway in the value is manifested by assuming a 1%

level of significance. So the values still is within the limit. Therefore, REJECT Ho.

2. By our definition of random variable:

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3. Roll a fair four sided die twice.

a. Give the joint probability distribution

f(x,y)

Total (must be

equal to 1)

0.0625

0.25

0.0625

0.25

y 3

0.0625

0.25

0.0625

0.25

1.0

b. Find the covariance. First, find the means of y and x alone and use the formula

prescribed:

The covariance has the following formula of:

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4. a. From the principle, the sum of the probabilities must be equal to 1. Hence,

Then we will apply the normal integration rules as in the following:

The resulting

And then c=0.0424

The technique for this lies similarly on the above method wherein we make the

a one variable of treatment rather than dealing with a joint variation and hence a double

integral in an analytical sense. Therefore, by using the direct calculator method of

integration,

C. We are asked to setup only the integral for P(X+Y>4). This type of question cannot be

answered because of the absence of the parameters given. Setting up the integral will yield

the following:

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5. Using F-test,

Using the calculator, we can compute the s for each set:

Hence, we have F=0.9723. This one has a degrees of freedom of (6,5). From the table in the

book at 0.05 level of significance, the critical region is

Hence, the level of value describes the difference between the two parameters in consideration.

This test gives us the consideration between similarities of the variances between two groups

who underwent almost a duplicated treatment. If the comparison between the table and the ones

calculated differ by greater or lesser values, then it is said to significantly different.

6. The random variable estimators are point estimate proportions of the chosen random

variable which will explicitly illustrate the analysis of magnitude inferences of the

respective set of data. Hence, a substitution is warranted for only case where data are

known and an expression relating the point estimates are available. Therefore, the answer

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to number 3 is as shown. The interval for x range from 0+2/no. of dat. In this case,

2/7=0.29

The table of values are as shown in the following:

.29

0.58

0.87

1.16

1.45

1.74

0.8

0.251

0.381

0.485

0.577

0.660

0.736

1.2

0.081

0.212

0.374

0.560

0.765

0.987

0.2

0.637

0.42

0.33

0.277

0.243

0.217

0.5

0.29

0.500

0.5

0.50

0.500

1.6

0.500

0.105

0.256

0.483

0.789

1.178

0.9

1.600

0.334

0.462

0.582

0.696

0.805

1.4

0.677

0.151

0.313

0.525

0.785

1.090

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