Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 13.3 minutes. The standard deviation of completion times was 1.6 minutes. An analyst at the company suspects that, under new management, the mean completion time, u, is now less than 13.3 minutes. To test this claim, a random sample of 20 completion times under new management was taken by the analyst. The sample had a mean of 12.6 minutes. Assume that the population is normally distributed. Can we support, at the 0.10 level of significance, the claim that the population mean completion time under new management is less than 13.3 minutes? Assume that the population standard deviation of completion times has not changed under new management. Perform a one-tailed test. Then complete the parts below. a. State the null hypothesis and the alternative hypothesis. b. Determine the type of test statistic to use. c. Find the value of the test statistic. (Round to three or more decimal places.) d. Find the critical value. (Round to three or more decimal places.) e. Can we support the claim that the population mean completion time under new management is less than 13.3 minutes? (Yes or No?)
Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 13.3 minutes. The standard deviation of completion times was 1.6 minutes. An analyst at the company suspects that, under new management, the mean completion time, u, is now less than 13.3 minutes. To test this claim, a random sample of 20 completion times under new management was taken by the analyst. The sample had a mean of 12.6 minutes. Assume that the population is normally distributed. Can we support, at the 0.10 level of significance, the claim that the population mean completion time under new management is less than 13.3 minutes? Assume that the population standard deviation of completion times has not changed under new management. Perform a one-tailed test. Then complete the parts below. a. State the null hypothesis and the alternative hypothesis. b. Determine the type of test statistic to use. c. Find the value of the test statistic. (Round to three or more decimal places.) d. Find the critical value. (Round to three or more decimal places.) e. Can we support the claim that the population mean completion time under new management is less than 13.3 minutes? (Yes or No?)
Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 13.3 minutes. The standard deviation of completion times was 1.6 minutes. An analyst at the company suspects that, under new management, the mean completion time, u, is now less than 13.3 minutes. To test this claim, a random sample of 20 completion times under new management was taken by the analyst. The sample had a mean of 12.6 minutes. Assume that the population is normally distributed. Can we support, at the 0.10 level of significance, the claim that the population mean completion time under new management is less than 13.3 minutes? Assume that the population standard deviation of completion times has not changed under new management. Perform a one-tailed test. Then complete the parts below. a. State the null hypothesis and the alternative hypothesis. b. Determine the type of test statistic to use. c. Find the value of the test statistic. (Round to three or more decimal places.) d. Find the critical value. (Round to three or more decimal places.) e. Can we support the claim that the population mean completion time under new management is less than 13.3 minutes? (Yes or No?)
1. Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 13.3 minutes. The standard deviation of completion times was 1.6 minutes. An analyst at the company suspects that, under new management, the mean completion time, u, is now less than 13.3 minutes. To test this claim, a random sample of 20 completion times under new management was taken by the analyst. The sample had a mean of 12.6 minutes. Assume that the population is normally distributed. Can we support, at the 0.10 level of significance, the claim that the population mean completion time under new management is less than 13.3 minutes? Assume that the population standard deviation of completion times has not changed under new management. Perform a one-tailed test. Then complete the parts below.
a. State the null hypothesis and the alternative hypothesis.
b. Determine the type of test statistic to use.
c. Find the value of the test statistic. (Round to three or more decimal places.)
d. Find the critical value. (Round to three or more decimal places.)
e. Can we support the claim that the population mean completion time under new management is less than 13.3 minutes? (Yes or No?)
2. An old medical textbook states that the mean sodium level for healthy adults is 139 mEq per liter of blood. A medical researcher believes that, because of modern dietary habits, the mean sodium level for healthy adults,u, now differs from that given in the textbook. A random sample of 90 healthy adults is evaluated. The mean sodium level for the sample is 140 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 10 mEq. Can we conclude, at the 0.05 level of significance, that the population mean adult sodium level differs from that given in the textbook? Perform a two-tailed test. Then complete the parts below.
a. State the null hypothesis and the alternative hypothesis.
b. Determine the type of test statistic to use.
c. Find the value of the test statistic. (Round to three or more decimal places.)
d. Find the p-value. (Round to three or more decimal places.)
e. Can we conclude that the population mean adult sodium level differs from that given in the textbook? (yes or no?)
Also please answer the 2 different questions attached by picture. Thank you!
Transcribed Image Text:For a certain knee surgery, a mean recovery time of 13 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time,
μ, is less than 13 weeks. In a random sample of 32 knee surgery patients who practiced this new physical therapy, the mean recovery time is 12.6 weeks.
Assume that the population standard deviation of recovery times is known to be 1.1 weeks.
Is there enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks?
Perform a hypothesis test, using the 0.10 level of significance.
(a) State the null hypothesis Ho and the alternative hypothesis H₁.
Ho:
H₁:
Standard Normal Distribution
Step 1: Select one-tailed or two-tailed.
O One-tailed
O Two-tailed
I
Step 2: Enter the critical value(s).
(Round to 3 decimal places.)
O<O
Step 3: Enter the test statistic.
(Round to 3 decimal places.)
☐20
X
• The test statistic has a normal distribution and the value is given by z=
x-μ
0
X
Oso
(b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your
test.
• Z0.10 is the value that cuts off an area of 0.10 in the right tail.
0.3+
0.2+
0.1-
0
□<ロ
3
#0
(c) Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the researcher.
O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough
evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy
is less than 13 weeks.
O Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not
enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical
therapy is less than 13 weeks.
O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is
enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical
therapy is less than 13 weeks.
O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is
not enough evidence to support the claim that the mean recovery time of patients who practice the new style of
physical therapy is less than 13 weeks.
X
Transcribed Image Text:A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean lifetime, μ, of 12 years. To test the
company's claim, a competitor has selected 35 of these batteries at random. The mean lifetime of the sample is 10.8 years. Suppose the population standard
deviation of these lifetimes is known to be 2.7 years.
Is there enough evidence to reject the claim that the mean lifetime of the newest model is 12 years? Perform a hypothesis test, using the 0.10 level of
significance.
(a) State the null hypothesis Ho and the alternative hypothesis H₁.
Ho:
H₁:0
• 20.05
value that cuts off area of 0.05 in the right tail.
Standard Normal Distribution
Step 1: Select one-tailed or two-tailed.
O One-tailed
O Two-tailed
μ
• The test statistic has a normal distribution and the value is given by z=
Step 2: Enter the critical value(s).
(Round to 3 decimal places.)
(b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your
test.
Step 3: Enter the test statistic.
(Round to 3 decimal places.)
O<O OSO O>O
ロミロ
X
ロ=ロ
x-μ
0
0.3+
0.2+
0#0
0.1+
S
X
(c) Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the company.
O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough
evidence to reject the claim that the mean lifetime of the newest model of battery is 12 years.
O Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not
enough evidence to reject the claim that the mean lifetime of the newest model of battery is 12 years.
O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is
enough evidence to reject the claim that the mean lifetime of the newest model of battery is 12 years.
O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is
not enough evidence to reject the claim that the mean lifetime of the newest model of battery is 12 years.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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