Helmet Telecom Ltd. claims that, on average, their new design for a wireless router has increased the speed to at least 1.70 Gbps, a big improvement over 1.50 Gbps maximum of the previous version. An independent testing laboratory in Hamilton found that a random sample of 12 of the newest version routers delivered speed of 1.64 Gbps, on average, with a standard deviation of 0.09 Gbps. Test the manufacturer's claim using a 0.03 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 hypothesis is the claim and what is the type of the test. H0H0: Select an answer p x s ? = < > H1H1: Select an answer p s x? < > = Which one is the claim?

• H1H1
• H0H0

The test isSelect an answer two-tailed right-tailed left-tailed.

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 H0H0 and fail to support H1H1 (claim)
• Fail to reject H0H0 (claim) and fail to support H1H1
• Fail to reject H0H0 and support H1H1 (claim)
• Reject H0H0 (claim) and support H1H1

(e) Select the correct statement.

• We prove that the average speed is still 1.50 Gbps.
• At 0.03 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 1.70 Gbps.
• At 0.03 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 1.70 Gbps.
• We are sure that, on average, the speed is at most 1.50 Gbps.
• None of the above.