Question

Some sports that involve a significant amount of running, jumping, or hopping put participants at risk...

Some sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendinopathy (AT), an inflammation and thickening of the Achilles tendon. A study looked at the diameter (in mm) of the affected tendons for patients who participated in these types of sports activities. Suppose that the Achilles tendon diameters in the general population have a mean of 5.95 millimeters (mm). When the diameters of the affected tendon were measured for a random sample of 34 patients, the average diameter was 9.50 with a standard deviation of 1.98 mm. Is there sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm? Test at the 5% level of significance.

State the null and alternative hypotheses.

H0: μ < 5.95 versus Ha: μ > 5.95

H0: μ = 5.95 versus Ha: μ > 5.95

H0: μ = 5.95 versus Ha: μ ≠ 5.95

H0: μ ≠ 5.95 versus Ha: μ = 5.95

H0: μ = 5.95 versus Ha: μ < 5.95

Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statistic z =

rejection region

z >

z <

State your conclusion.

H0 is rejected. There is insufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm. H0 is not rejected. There is insufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm.

H0 is not rejected. There is sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm.

H0 is rejected. There is sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm.

Homework Answers

Answer #1

Solution:
Null hypothesis is H0: mean = 5.95
Alternate hypothesis is H1: mean > 5.95
test statistic = (9.5-5.95)/1.98/sqrt(34) = 10.45
at alpha = 0.05 this is a right tailed test so Z at 0.05 is 1.645
If test statistic is greater than 1.645 than reject null hypothesis else do not reject the null hypothesis.
As we can see that Ztest>1.645, So H0 is rejected. there is sufficient evidence to indicate that the average diameter of the tenfon for patients with AT is greater than 5.595 mm.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Some sports that involve a significant amount of running, jumping, or hopping put participants at risk...
Some sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendinopathy (AT), an inflammation and thickening of the Achilles tendon. A study looked at the diameter (in mm) of the affected tendons for patients who participated in these types of sports activities. Suppose that the Achilles tendon diameters in the general population have a mean of 5.95 millimeters (mm). When the diameters of the affected tendon were measured for a random sample...
Some sports that involve a significant amount of running, jumping, or hopping put participants at risk...
Some sports that involve a significant amount of running, jumping, or hopping put participants at risk of Achilles tendinopathy (AT), an inflammation and thickening of the Achilles tendon. A study in the American Journal of Sports Medicine looked at the diameter (in mm) of the affected tendons for patients who participated in these types of sports activities. Suppose that the Achilles tendon diameters in the general population have a mean of 5.97 millimetres. When the diameters of the affected tendon...
Acid rain—rain with a pH value less than 5.7, caused by the reaction of certain air...
Acid rain—rain with a pH value less than 5.7, caused by the reaction of certain air pollutants with rainwater—is a growing problem in the United States. Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure of acidity: 0 is acid; 14 is alkaline). A sample of n = 30 rainfalls produced pH readings with x = 3.7 and s = 0.5. Do the data provide sufficient evidence to indicate that the mean pH...
Many companies are becoming involved in flextime, in which a worker schedules his or her own...
Many companies are becoming involved in flextime, in which a worker schedules his or her own work hours or compresses work weeks. A company that was contemplating the installation of a flextime schedule estimated that it needed a minimum mean of 7 hours per day per assembly worker in order to operate effectively. Each of a random sample of 90 of the company's assemblers was asked to submit a tentative flextime schedule. If the mean number of hours per day...
A random sample of 100 observations from a quantitative population produced a sample mean of 21.5...
A random sample of 100 observations from a quantitative population produced a sample mean of 21.5 and a sample standard deviation of 8.2. Use the p-value approach to determine whether the population mean is different from 23. Explain your conclusions. (Use α = 0.05.) State the null and alternative hypotheses. H0: μ = 23 versus Ha: μ < 23 H0: μ = 23 versus Ha: μ > 23 H0: μ = 23 versus Ha: μ ≠ 23 H0: μ <...
To properly treat patients, drugs prescribed by physicians must not only have a mean potency value...
To properly treat patients, drugs prescribed by physicians must not only have a mean potency value as specified on the drug's container, but also the variation in potency values must be small. Otherwise, pharmacists would be distributing drug prescriptions that could be harmfully potent or have a low potency and be ineffective. A drug manufacturer claims that his drug has a potency of 5 ± 0.1 milligram per cubic centimeter (mg/cc). A random sample of four containers gave potency readings...
To properly treat patients, drugs prescribed by physicians must not only have a mean potency value...
To properly treat patients, drugs prescribed by physicians must not only have a mean potency value as specified on the drug's container, but also the variation in potency values must be small. Otherwise, pharmacists would be distributing drug prescriptions that could be harmfully potent or have a low potency and be ineffective. A drug manufacturer claims that his drug has a potency of 5 ± 0.1 milligram per cubic centimeter (mg/cc). A random sample of four containers gave potency readings...
Independent random samples of n1 = 170 and n2 = 170 observations were randomly selected from...
Independent random samples of n1 = 170 and n2 = 170 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 96 successes, and sample 2 had 103 successes. You wish to perform a hypothesis test to determine if there is a difference in the sample proportions p1 and p2. (a) State the null and alternative hypotheses. H0: (p1 − p2) < 0 versus Ha: (p1 − p2) > 0 H0: (p1 − p2) = 0...
Industrial wastes and sewage dumped into our rivers and streams absorb oxygen and thereby reduce the...
Industrial wastes and sewage dumped into our rivers and streams absorb oxygen and thereby reduce the amount of dissolved oxygen available for fish and other forms of aquatic life. One state agency requires a minimum of 5 parts per million (ppm) of dissolved oxygen in order for the oxygen content to be sufficient to support aquatic life. Six water specimens taken from a river at a specific location during the low-water season (July) gave readings of 4.9, 5.0, 5.0, 5.1,...
An experiment was conducted to test the effect of a new drug on a viral infection....
An experiment was conducted to test the effect of a new drug on a viral infection. After the infection was induced in 100 mice, the mice were randomly split into two groups of 50. The first group, the control group, received no treatment for the infection, and the second group received the drug. After a 30-day period, the proportions of survivors, p?1 and p?2, in the two groups were found to be 0.38 and 0.66, respectively. (a) Is there sufficient...