The Result of a Hypothesis Is Described in Terms of the Probability

question 197

Essay

The result of a hypothesis is described in terms of the probability of obtaining a particular sample. Use the given contextto formulate the null and alternative hypotheses. Discuss whether the sample provides evidence for rejecting the nullhypothesis.
-In the city of Heathville, the proportion of births that are by Caesarean section is $0.23$ (23\%). A small private hospital claims that at their hospital, the proportion of Caesarean births is lower. In a random sample of 120 births at the private hospital, the proportion of Caesarean births was $0.18$ .
Assuming that the true proportion of Caesarean births at the private hospital is $0.23$ , the probability of selecting a sample in which the proportion of Caesareans is $0.18$ or less is roughly $0.09$ .

Understand the characteristics of multinomial experiments and their relevance to chi-square tests.

Calculate degrees of freedom and understand its importance in chi-square tests.

Recognize the importance of sample size and design in assessing statistical tests.

Understand the principles and application of chi-square tests of independence and goodness-of-fit tests.

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Definitions:

Spread

A term referring to the range or distribution of a set of data points or values, indicating how far apart data points are.

Histograms

A type of graphical representation of data distribution using bars of different heights to illustrate the frequency of data points within certain ranges.

Original Data

The initial dataset collected or observed before any processing, analysis, or transformation is applied.

Skewed Histogram

A graphical representation of data that is not symmetrical and leans towards one side, indicating a lack of normal distribution.