Q 4.19: To verify whether there are negative consequences of taking a new type of medicine, 3000 tests were conducted. Assume that the null hypothesis is that the new medicine has no negative effects and the alternative hypothesis is that the new medicine is potentially harmful. 31 of these tests gave significant results at a 1% significance level. What can we say about the potential harmfulness of the new medicine

The p-value obtained is less than the significance level at which the test was performed at, hence, we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.

Step-by-step explanation:

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that the new medicine has no negative effects and the alternative hypothesis is that the new medicine is potentially harmful

Mathematically,

The null hypothesis is represented as

H₀: p = 0

The alternative hypothesis is represented as

Hₐ: p > 0

To do this test, we will use the z-distribution because although no information on the population standard deviation is known, the sample size is large enough.

So, we compute the test statistic

z = (x - μ)/σₓ

x = sample proportion = (31/3000) = 0.0103

μ = p₀ = 0

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 3000

σₓ = √[0.0103×0.9897/3000] = 0.0018462936 = 0.0018463

z = (0.0103 - 0) ÷ 0.0018463

z = 5.60

checking the tables for the p-value of this test statistic

Significance level = 1% = 0.01

The hypothesis test uses a one-tailed condition because we're testing only in one direction.

p-value (for z = 5.60, at 0.01 significance level, with a one tailed condition) = < 0.00001

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.01

p-value = < 0.00001

p-value < 0.00001 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.

Hope this Helps!!!

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.

javeir earned 56 dollors more than kyle so kyle and javier had 14w but javier made 56 dollors more so 14w plus 56 equals 70w so kyle has 14w

step-by-step explanation: hope i plz give me brainliest with the points so this is not constant cause it says last week so its clearly not every week