Problem Solving. (Choose Two from the following three questions; 4 points each.)

Question

Problem Solving. (Choose Two from the following three questions; 4 points each.). In early 1990s. the mean Body Mass Index (BMI) for children 16 or 17 years of age in America is 22 3 The researcher intends to find out whether our children have grown more obese over the past two decades, so she sampled 25 teens of 16 or 17 years old The results from the sample showed that the mean BMI is 22.9 with a standard deviation of 1.2. a. What is the research question in this research? b. State the null and alternative hypothesis c. Calculate the test statistics and find out the T value d Consult the T table and state the conclusion (at 95% confidence level) A pharmaceutical company has produced an experimental medicine to control cancer cells from replication with a success rate of 90%. The medicine is administered to 20 cancer patients in a clinical trial (The trail for the 20 patients is independent.) Let X be the number of patents whose cancer cells stopped replication. a. What type of probability distribution is the rate of success would follow? Explain why? b. What is the probability that live medicine will control cancer cell replication for all of the 20 patients? What is the probability 10 patients? The blood pressures (Diastolic mm Hg) of a random sample of 9 patients are presented below. A. What is the mean blood pressure for the sample? B. What is the standard deviation of the sample blood pressure? C. Construct a confidence interval (95%) for mean Diastolic blood pressure for all the patients.

Explanation / Answer

answering only 1st question

Set Up Hypothesis
Null, H0: U<22.3
Alternate, it is grown more, H1: U>22.3
Test Statistic
Population Mean(U)=22.3
Sample X(Mean)=22.9
Standard Deviation(S.D)=1.2
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =22.9-22.3/(1.2/Sqrt(25))
to =2.5
| to | =2.5
Critical Value
The Value of |t | with n-1 = 24 d.f is 1.711
We got |to| =2.5 & | t | =1.711
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 2.5 ) = 0.00983
Hence Value of P0.05 > 0.00983,Here we Reject Ho

d.
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=22.9
Standard deviation( sd )=1.2
Sample Size(n)=25
Confidence Interval = [ 22.9 ± t a/2 ( 1.2/ Sqrt ( 25) ) ]
= [ 22.9 - 2.064 * (0.24) , 22.9 + 2.064 * (0.24) ]
= [ 22.405,23.395 ]

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