Question

In: Statistics and Probability

6.         A pharmaceutical company makes a pill intended to reduce the chances of seizures             among...

6.         A pharmaceutical company makes a pill intended to reduce the chances of seizures

            among children. The pill is supposed to contain 20.0 mg of Phenobarbital. A simple

            random sample of 20 pills yielded the amounts listed here. Does this sample provide

            evidence that the mean amount of Phenobarbital is different than 20.0 mg? Use a 1%

            significance level.

27.5     26.0     22.9     23.4     23.0     23.9     32.6     20.9     22.9     24.3

24.8     16.1     24.3     17.3     18.9     20.7     33.0     15.6     24.3     23.3

Solutions

Expert Solution

Solution:

x x2
27.5 756.25
26 676
22.9 524.41
23.4 547.56
23 529
23.9 571.21
32.6 1062.76
20.9 436.81
22.9 524.41
24.3 590.49
24.8 615.04
16.1 259.21
24.3 590.49
17.3 299.29
18.9 357.21
20.7 428.49
33 1089
15.6 243.36
24.3 590.49
23.3 542.89
∑x=465.7 ∑x2=11234.37



Mean ˉx=∑xn

=27.5+26+22.9+23.4+23+23.9+32.6+20.9+22.9+24.3+24.8+16.1+24.3+17.3+18.9+20.7+33+15.6+24.3+23.3/20

=465.7/20

=23.285


Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√11234.37-(465.7)220/19

=√11234.37-10843.8245/19

=√390.5455/19

=√20.555

=4.5338

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 20

Ha :     20

Test statistic = t

= ( - ) / S / n

= (23.28-20) /4.53 / 20

= 3.238

Test statistic = t = 3.238

P-value =0.0043

= 0.01

P-value <

0.0043 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that


Related Solutions

A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2...
A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of ?¯=143 with standard deviation ?=21 . Is this sufficient evidence that the diet is effective in meeting the target? Assume the distribution of the...
A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2...
A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of ¯ x = 143 with standard deviation s = 21 . Is this sufficient evidence that the diet is effective in meeting the target?...
A pharmaceutical company developed a new revolutionary diet pill, “fat buster,” which is believed to greatly...
A pharmaceutical company developed a new revolutionary diet pill, “fat buster,” which is believed to greatly help people with losing weights. They conducted an experimental study to assess its relative effectiveness, comparing it with a currently popular diet pill in the market. A random sample of 28 participants were split into two groups: People in Group A used this company’s “fat buster” and those in Group B used a competing diet pill, “fat killer.” After taking the pills for 6...
A new potential heart medicine, code-named X-281, is being tested by a pharmaceutical company, Pharma-pill. As...
A new potential heart medicine, code-named X-281, is being tested by a pharmaceutical company, Pharma-pill. As a research technician at Pharma-pill, you are told that X-281 is a monoprotic weak acid, but because of security concerns, the actual chemical formula must remain top secret. The company is interested in the drug's Ka value because only the dissociated form of the chemical is active in preventing cholesterol buildup in arteries. To find the pKa of X-281, you prepare a 0.089 M...
A new potential heart medicine, code-named X-281, is being tested by a pharmaceutical company, Pharma-pill. As...
A new potential heart medicine, code-named X-281, is being tested by a pharmaceutical company, Pharma-pill. As a research technician at Pharma-pill, you are told that X-281 is a monoprotic weak acid, but because of security concerns, the actual chemical formula must remain top secret. The company is interested in the drug's Ka value because only the dissociated form of the chemical is active in preventing cholesterol buildup in arteries. To find the pKa of X-281, you prepare a 0.089 M...
105. A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of...
105. A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. a. i. x = __________ ii. sx = __________ iii. n = __________ iv. n – 1 = __________ b....
A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time...
A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.9; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you...
QUESTION 3: A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length...
QUESTION 3: A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7, 2.8, 3.0, 2.3, 2.3, 2.2, 2.8, 2.1 and 2.4. a) Find the mean of the sample. b) Find the standard deviation of the sample. c) Find the median...
Question 3 (Total 6 marks) Biogen Pharmaceutical Ltd is a large pharmaceutical company based in Australia....
Question 3 (Total 6 marks) Biogen Pharmaceutical Ltd is a large pharmaceutical company based in Australia. During the year ending 30 June 2020, Biogen Pharmaceutical Ltd purchased two electronic databases containing scientific data related to respiratory drugs. Database A was acquired for $1,000,000 and contains data that is copyright protected. Database B was acquired for $800,000 and contains data that is not copyright protected. Required (a) Explain whether Database A and Database B satisfy: (i) The definition of an intangible...
Suppose that a pharmaceutical company makes the assertion that Drug A has a stronger effect than...
Suppose that a pharmaceutical company makes the assertion that Drug A has a stronger effect than Drug B. To test this claim, 1000 randomly selected people were given the two drugs during different treatment periods. Among them, 600 preferred taking Drug A because of the stronger effect they felt; whereas 400 preferred Drug B. Determine whether there is sufficient evidence, at the 5% level of significance, to support the company’s claim that Drug A is stronger and preferred by more...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT