to recover from the cold was recorded. At the end of the experiment the following data were obtained. Days to recover from a cold Treated with old tablet 3.0, 3.3, 4.3, 5.6, 5.3, 8.3, 3.7, 5.2, 5.3, 8.9, 6.3, 2.5, 3.3, 4.0, 4.8, 1.7, 4.9, 2.1, 3.7, 5.1, 4.9, 3.8, 2.4, 4.3, 5.6 Treated with new tablet 5.3, 4.0, 5.5, 3.8, 7.2, 1.8, 4.9, 6.2, 5.0, 4.7, 5.5, 6.9, 4.0, 4.5, 6.4, 2.8, 4.7, 6.4, 3.2, 5.7, 4.5, 7.0, 3.8, 6.0, 6.1 Send data to calculator Send data to Excel It is known that the population standard deviation of the recovery time from a cold is 1.8 days when treated with the old tablet, and the population standard deviation of the recovery time from a cold is 1.5 days when treated with the new tablet. It is also known that both populations are approximately normally distributed. At the 0.05 level of significance, is there enough evidence to support the claim that the mean recovery time, μ₁, of all patients treated with the old tablet is more than the mean recovery time, μ₂, of all patients treated with the new tablet? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho O H₁ (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the researchers' claim that the mean recovery time when treated with the old tablet is more than the mean recovery time when treated with the new tablet? O Yes O No Н |x X a S X On 0=0 OSO 0#0 O

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2CYU

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A pharmaceutical company sells a tablet for treating colds. After extensive experimentation, researchers at the pharmaceutical company have developed a new formula for the tablet. The researchers suspect that the mean recovery time of all patients treated with the old tablet is more than the mean recovery time of all patients who are treated with the new tablet. To see if this is true, a random selection of volunteers were exposed to a typical cold virus. After they started to have cold symptoms, 25 of them were given the old tablet. The remaining 25 volunteers were given the new tablet. For each individual, the length of time taken to recover from the cold was recorded. At the end of the experiment the following data were obtained.

It is known that the population standard deviation of the recovery time from a cold is 1.8 days when treated with the old tablet, and the population standard deviation of the recovery time from a cold is 1.5 days when treated with the new tablet. It is also known that both populations are approximately normally distributed. At the 0.05 level of significance, is there enough evidence to support the claim that the mean recovery time, μ1, of all patients treated with the old tablet is more than the mean recovery time, μ2, of all patients treated with the new tablet? Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)

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to recover from the cold was recorded. At the end of the experiment the following data were obtained.
Days to recover from a cold
Treated with old tablet 3.0, 3.3, 4.3, 5.6, 5.3, 8.3, 3.7, 5.2, 5.3, 8.9, 6.3, 2.5, 3.3, 4.0, 4.8, 1.7, 4.9, 2.1, 3.7, 5.1, 4.9, 3.8, 2.4, 4.3, 5.6
Treated with new tablet 5.3, 4.0, 5.5, 3.8, 7.2, 1.8, 4.9, 6.2, 5.0, 4.7, 5.5, 6.9, 4.0, 4.5, 6.4, 2.8, 4.7, 6.4, 3.2, 5.7, 4.5, 7.0, 3.8, 6.0, 6.1
Send data to calculator V Send data to Excel
It is known that the population standard deviation of the recovery time from a cold is 1.8 days when treated with the old tablet, and the population standard
deviation of the recovery time from a cold is 1.5 days when treated with the new tablet. It is also known that both populations are approximately normally
distributed. At the 0.05 level of significance, is there enough evidence to support the claim that the mean recovery time, μ₁, of all patients treated with the old
tablet is more than the mean recovery time, μ₂, of all patients treated with the new tablet? Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis Ho and the alternative hypothesis H₁.
Ho :O
H₁ :0
(b) Determine the type of test statistic to use.
(Choose one) ▼
(c) Find the value of the test statistic. (Round to three more decimal places.)
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(d) Find the p-value. (Round to three or more decimal places.)
(e) Can we support the researchers' claim that the mean recovery time when
treated with the old tablet is more than the mean recovery time when
treated with the new tablet?
O Yes O No
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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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