Question

1)Determine whether the following statement is true or​ false: The Z score of a value measures how many standard deviations the value is from the mean.

True

False

2)A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

​Gotham:

Upper X overbarXSubscript Upper GGequals=35

​months,

Upper S Subscript Upper G Superscript 2S2Gequals=900

    ​ Metropolis:

Upper X overbarXSubscript Upper MMequals=50

​months,

Upper S Subscript Upper M Superscript 2S2Mequals=1050

Suppose

alphaαequals=0.10.

Which of the following represents the result of the relevant hypothesis​ test?

A.

The null hypothesis is not rejected.

B.

The null hypothesis is rejected.

C.

The alternative hypothesis is rejected.

3)How is the method of moving averages is​ used?

A.

To plot a series

B.

To smooth a series

C.

To exponentiate a series

D.

In regression analysis

D.

Insufficient information exists on which to make a decision.

4)An alcohol awareness task force at a BigTen university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend​ studying, and whether they did well or poorly on the midterm. The results are shown below.

	Did Well on Midterm	Did Poorly on Midterm
Studying for Exam	80	20
Went Bar Hopping	30	70

What is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the​ midterm?

A.

​(30plus+​70)/200

or

​(70plus+​30)/200

or​ 50%

B.

​(80plus+​30)/200

or

​(30plus+​80)/200

or​ 55%

C.

​30/200 or​ 15%

D.

​(80plus+30plus+​70)/200

or

​(110plus+100minus−​30)/200

or​ 90%

5)

The overall upward or downward pattern of the data in an annual time series will be contained in the​ ________ component.

A.

trend

B.

irregular

C.

cyclical

D.

seasonal

Answer 1

1)

Answer)

Z = (x - mean)/(s.d)

X = mean + (Z*s.d)

So, yes z score is a value of measures, how many standard deviations the value is from the mean

True

2)

Null hypothesis Ho : u1 = u2

Alternate hypothesis Ha : u1 < u2

When the population variances are equal

Then test statistics is = (x1-x2)/standard error

Where standard error = sp√{(1/n1)+(1/n2)}

Sp = √{(n1-1)*s1^2 + (n2-1)*s2^2 }/√{n1+n2-2}

Test statistics t = -3.69

Degrees of freedom is = n1+n2-2 = 248

For 248 dof and -3.69 test statistics

P-value from.t distribution is 0.000138

As the p-value is less than the given significance 0.1

We reject the null hypothesis