Question

In: Statistics and Probability

A company ran tests of its current internal computer network. Thirty files ranging in size from...

A company ran tests of its current internal computer network. Thirty files ranging in size from 29 to 100 megabytes (MB) were transmitted over the network at various times of day, and the time to send the files recorded, as shown in the accompanying data table. Formulate the SRM with Y given by Transfer Time and X given by File Size. Complete parts (a) through (c) below.

File size (MB)	Time (sec)
67	31.7
66	30.6
25	16.4
53	24.1
87	37.1
32	19.2
80	33.2
23	14.6
35	20.1
29	14.6
64	27.2
55	26.2
44	19.2
91	37.2
21	11.9
91	33.8
49	20.5
28	18.7
50	24.3
34	19.1
98	36.7
34	20.4
48	22.7
44	19.2
74	32.3
55	27.6
38	21.1
42	18.7
63	29.5
66	30.9

(a) Is the correlation between file size and transfer time significantly different from zero?

Identify the hypotheses to be tested. Choose the correct answer below.

A. H0 : β1 ≠ 0
HA :β1 = 0

B. H0 : β1 ≤ 0
HA: β1= 0

C. H0 : β1 = 0
HA: β1 > 0

D. H0: β1 ≥ 0
HA: β1 = 0

E. H0: β1 = 0
HA: β1< 0

F. H0: β1= 0
HA: β1≠ 0

Find the value of the test statistic t associated with beta β1.

t = ____ (Round to two decimal places as needed.)

Find the p-value for this test.

p-value = _____ (Round to four decimal places as needed.)

Determine whether the correlation between file size and transfer time differs significantly from zero. Choose the correct answer below.

A. Do not reject H0. There is insufficient evidence that the correlation between file size and transfer time is not zero.

B.Do not reject H0. There is sufficient evidence that the correlation between file size and transfer time is not zero.

C.Reject H0. There is sufficient evidence that the correlation between file size and transfer time is not zero.

D.Reject H0. There is insufficient evidence that the correlation between file size and transfer time is not zero.

______________________________________________________________________________________________________________________________________

(b) Estimate the average "setup" time to start the file transfer. This time is used to synchronize the computers making the transfer and is unrelated to file size. Use a confidence level of 95%.

The average setup time is _____ to ________ seconds. (Round to one decimal place as needed.)

______________________________________________________________________________________________________________________________________

(c) To speed transfers, the company introduced compression software that halves the size of a file when sent over the network. On average, what is the improvement in time when sending a 50-MB file? State your answer as a range.

On average, the improvement in time is _____ to ______ seconds. (Round to one decimal place as needed.)

Expert Solution

orchestra answered 2 years ago

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