Question

. (30 pts) Write an appropriate hypothesis testing problem that’s related to your article for the population small sample mean.. You are free to choose a one‐sided or a two‐sided alternative. (10 pts)

a. State the null and alternative hypotheses. (5 pts)

b. Compute the test statistic under the assumption that the null hypothesis is true. Use two decimal places for ? scores and three decimal places for ? and ? values. (5 pts)

c. Compute the ?‐?????. (5 pts) d. State a conclusion for ?%(8) significance level.

I will use your question and solution as a guide. So it do not need to be original. Thank you! You should please write your own question. Then solve it thanks

Answer 1

ANSWER::

Suppose the research is to test a new medication to see if it has either a positive or negative impact on intelligence of students of class 10th, or it has no effect at all. To test this, IQ of students of class 10th is considered.

It is known that in general, the average IQ of students is 100.

A sample of 20 students is considered who were administered the new medication. Their IQ turned out to be 140 with a standard deviation of 20.

Our problem is to check if the medication affected intelligence or not is to be tested.

As the samplesize is 20, it is a small sample problem.

a)

H0: Medication had no effect on intelligence.

ie. H0: Medication had either a positive or negative impact on intelligence

From article we have n=20 (small sample as n<30); sample std. dev. (s)= 20, sample mean = 140

Let, alpha = level of significance = 8%

b)

Test statistic under null hypothesis for the above problem is given as

Under H0, t ~ t distribution with (n-1) = 19 d.f.

Thus, t-score for 8% level of significance (using t table) is P(t > tcritical) = 0.08/2 = 0.04

tcritical = +-1.8495

Decision rule: Reject H0 if t is less than -1.8495 or if t is greater than +1.8495

d) As t = 8.944 > tcritical = 1.8495; We reject H0.

c)

p-value: 2*P(t19>8.944) = 2*0.000 = 0 (p-value is multiplied by 2 as the hypothesis is two-sided)

d)

As p-value = 0 < 0.08; We reject H0 at 8% l.o.s

CONCLUSION: Thus, the test states that we have enough evidence to say that the new medication has either a positive or negative impact on intelligence (infered using IQ score) of students of class 10th.

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