Helmet Telecom Ltd. claims that, on average, their new design for a wireless router has increased the speed to at least 1.9 Gbps, a big improvement over 1.5 Gbps maximum of the previous version. An independent testing laboratory in Etobicoke found that a random sample of 10 of the newest version routers delivered speed of 1.83 Gbps, on average, with a standard deviation of 0.1 Gbps. Test the manufacturer's claim using a 0.01 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.
Helmet Telecom Ltd. claims that, on average, their new design for a wireless router has increased the speed to at least 1.9 Gbps, a big improvement over 1.5 Gbps maximum of the previous version. An independent testing laboratory in Etobicoke found that a random sample of 10 of the newest version routers delivered speed of 1.83 Gbps, on average, with a standard deviation of 0.1 Gbps. Test the manufacturer's claim using a 0.01 significance level. Assume that the speeds are approximately
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.
H0H0:
H1H1:
Which one is the claim?
- H1H1
- H0H0
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?
- Fail to reject H0H0 (claim) and fail to support H1H1
- Reject H0H0 (claim) and support H1H1
- Reject H0H0 and fail to support H1H1 (claim)
- Fail to reject H0H0 and support H1H1 (claim)
(e) Select the correct statement.
- At 0.01 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 1.9 Gbps.
- At 0.01 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 1.9 Gbps.
- We prove that the average speed is still 1.5 Gbps.
- We are sure that, on average, the speed is between 1.83 Gbps and 1.9 Gbps.
- None of the above.
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