Tilda Telecom Ltd. claims that, on average, their new design for a wireless router has increased the speed to at least 1.8 Gbps, a big improvement over 1.5 Gbps maximum of the previous version. An independent testing laboratory in Mississauga found that a random sample of 13 of the newest version routers delivered speed of 1.74 Gbps, on average, with a standard deviation of 0.09 Gbps. Test the manufacturer's claim using a 0.025 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, identify which one is the claim and type of the test.

H0

:

H1:

Which one is the claim?

• H0

The test is

.

For parts (b), (c) use the correct sign for the critical t-value and test statistic.

(b) What is the critical t-value?

(c) What is the test statistic?

(d) Is the null hypothesis rejected? Is the alternative hypothesis supported?

• Reject H0

(claim) and support H1 and fail to support H1 (claim) and fail to support H1 and support H1

• (claim)

(e) Select the correct statement.

• We prove that the average speed is still 1.5 Gbps.
• At 0.025 significance level, there is not sufficient evidence to warrant rejection of the claim that, on average, the new wireless router has increased the speed to at least 1.8 Gbps.
• At 0.025 significance level, there is sufficient sample evidence to warrant rejection of the claim that, on average, the new wireless router has increased the speed to at least 1.8 Gbps.
• We are sure that, on average, the speed is between 1.74 Gbps and 1.8 Gbps.
• None of the above.

H1

Reject H0

(claim)

Fail to reject H0

Fail to reject H0