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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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.)
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
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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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