# checking answers and solving 4 more

*label*Mathematics

*timer*Asked: Dec 14th, 2018

*account_balance_wallet*$15

**Question description**

I have the first document for Quiz2 where i have stated answers but not fully sure of them, or if i answered all parts of the equation. So I would like you to go over them and check them again and complete whats missing.

the next document contain 4 questions only i would like you so solve them please

thank you.

## Tutor Answer

Hi there :). I am back...here is your assignments :). Kindly open the attached files :)

Math 260

Quiz 2

Name: ____________________

Problem 1

Is there a difference in average miles traveled for each of two taxi companies

during a randomly selected week? The data are:

Yellow Cab Company

American United Company

X1=837

X2=753

σ =30

σ =40

n1=35

n2=40

Use α= 0.05. assume that the populations are normally distributed.

a. State the null Hypothesis.

Answer: 𝐻0 : 𝜇1 − 𝜇2 = 0

b. State the alternative hypothesis.

Answer: 𝐻1 : 𝜇1 − 𝜇2 ≠ 0

c. Is this a right-tailed test, Left-tailed, or a two-tailed test?

Answer: The hypothesis given would be two-tailed test.

d. Which statistical distribution applies for this problem?

Answer:

Decision rule: Reject H0 if test statistic value greater than critical value

e. Find the critical values? Show the critical values on the graph of the distribution, and

identify the rejection region and non-rejection region

Answer:

From the standard normal table, at 5% level of significance, the critical value would be

1.96 and below is the graph:

f. Compute the test values.

Answer:

1

Math 260

Quiz 2

𝑍0 =

Name: ____________________

̅̅̅1 − 𝑋

̅̅̅2 ) − (𝜇1 − 𝜇2 )

(𝑋

𝜎 2

√( 𝑛1 +

1

=

𝜎2 2

𝑛2

)

(837 − 753) − 0

302

√

35

+

402

40

84

=

8.1064

= 𝟏𝟎. 𝟑𝟔

g. Make your decision based the test vales and the critical values.

Answer:

The test statistic value is greater than the critical value (1.96). Hence, we reject the null

hypothesis at 5% level of significance.

h. Summarize the results.

Answer:

There is sufficient evidence that there is a difference in a an average miles traveled for

each two taxi companies during a randomly selected week.

Problem 2

Two brands of batteries are tested, and their voltages are compared. The summary

statistics follow. Find the 95% confidence interval of the true difference in the means. Assume

that both variables are normally distributed.

Exercise: Battery Voltage

Brand X

Brand Y

Answer:

̅ = 9.2 − 8.8 = 0.4

𝐷

0. 32 0. 12

0.4 + (1.96)√

+

< 𝜇1 − 𝜇2 <

27

30

0. 32 0. 12

√

0.4 + (1.96)

+

27

30

2

Math 260

Quiz 2

Name: ____________________

0.281 < 𝜇1 − 𝜇2 < 0.519

OR, 0.3 < 𝜇1 − 𝜇2 < 0.5

Problem 3 The number of murders and robberies per 100,000 population for a random

selection of states is shown. Is there a linear relationship between the variables?

Murders 2.4 2.7 5.6 2.6 2.13.3 6.6 5.7

Robberies 25.314.3151.691.1 80 49 17395.8

a. Draw the scatter plot for the variables.

Answer:

b. Compute the value of the correlation coefficient.

Answer:

Correlation coefficient=CORREL(x,y)=0.8043

c. State the hypotheses.

Answer:

d. Test the significance of the correlation coefficient at α = 0.05, using Table I.

3

Math 260

Quiz 2

Name: ____________________

Answer:

We notice that the sample size is 8, so, the we get ...

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