Will someone help me in my Statistics Quiz?
A researcher a medicalschool believes that Coffee consumption may increase the heart beat rate. Suppose it is known that the heart beat rate is normally distributed with an average of 70 for adults. A random sample of 25 adults was selected and it was found that their average heartbeat was 73 after coffee consumption, with a standard deviation of 7.
a) formulate the null and alternative hypothesis.
b) Test hypothesis in part A. at 10% significance level to determine if we can infer that coffee consumption increases heart beat rate.
c) what is the required condition (assumptions) of the technique used in part B?
The null hypothesis formulated is that there is no significant increase in the average heart beat after coffee consumption.
Ho : Mu = 70
The alternative hypothesis formulated is that there is a significant increase in the average heart beat after coffee consumption.
Ha : Mu > 70
Level of significance = alpha = a = 10% = 0.1
As the sample size is less than 30 i.e., Small sample , the student’s t-distribution OR t-test shall be taken as the test criterion.
t = (Xbar – Mu)*sqrt (sample size) / Standard deviation
= (73 – 70)*sqrt 25 / 7
= 3*5 / 7
= 2.14
Degrees of freedom = nu = v = n-1 = 25-1 = 24
Critical value or table value of t for v = 24 at a = 0.1 is 1.318 (One tailed test)
Since the calculated value of t (2.14) is greater than the critical value or table value of t (1.318), the null hypothesis will be rejected.
In other words it can be inferred that there is significant increase in the average heart beat after coffee consumption.
>>>>>>>>>>>>
Assumptions;
It is assumed that the parent population is normal even though the sample is a small sample. (Of course it is given in the question)
TAMU Computer Science: Coffe-e-mail
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