Pacific Telecom Ltd. claims that their new design for a wireless router has increased the speed toat least1700 Mbits/sec, a big improvement over 1300 Mbits/sec maximum of the previous version. An independent testing laboratory in Vancouver found that a random sample of 46 of the newest version routers delivered speed of 1648 Mbits/sec, on average, with a standard deviation of 102 Mbits/sec. Is there any evidence that the manufacturer's claim is false? Test the claim using a 1% significance level. Assume that the speeds are approximately normally distributed as the histogram of the sample values is roughly symmetric and bell-shaped, so t-distribution is applicable for hypothesis testing.

Round to 3 decimal places where appropriate.

(a) State the null and alternative hypotheses, and identify which one is the claim.

H

0

H0

:Select an answer

p

s

x

?

=

>

<

H

1

H1

:Select an answer

p

x

s

?

>

=

<

Which one is the claim:

• H
• 0
• H0
• H
• 1
• H1

For parts (b), (c) use the correct sign for the t-value and test statistic, either positive or negative.

(b) What is the critical t-value (from the Student t-table)?

(c) What is the test statistic (from the formula)?

(d) Is the null hypothesis rejected?

• No
• Yes

(e) Conclude:

• At 1% significance level, there is sufficient sample evidence to warrant rejection of the claim. The speed did increase to the extent company claimed.
• At 1% significance level, there is not sufficient evidence to warrant rejection of the claim. The speed may have increased to the extent company claimed.
• At 1% significance level, there is not sufficient evidence to warrant rejection of the claim. There is not enough evidence to conclude that the speed increased to the extent company claimed.
• At 1% significance level, there is sufficient sample evidence to warrant rejection of the claim. The speed did not increase to the extent company claimed.
• None of the above.