^{Hypothesis Testing (Parametric)}

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^{Md. Ershadul Haque}

^{Associate Professor}

^{Dept. of Statistics, University of Dhaka}

^{09-10 February, 2024�}

Hypothesis:

• A statement about a population parameter (population mean, population proportion, etc.) subject to verification.
• The purpose of hypothesis testing is to draw a conclusion about the population parameters for which we do not have complete knowledge.

Examples:

1. A production manager claims that a 500 mg tablet is overfilled.
2. A physician may hypothesize that the recommended drug is effective in more than 90% cases.
3. A bulb’s manufacturing company claims that a new bulb it has developed has an average lifetime that exceeds the current industry average of 8,000 hours.

Test of a Statistical Hypothesis:

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• A two-action decision rule based on sample observations. The rule can be used to determine whether the hypothesis is a reasonable statement.
• The two-actions being the acceptance or rejection of the hypothesis under consideration.
• If the hypothesis is reasonable, we would accept it, otherwise it would be rejected.
• Two mutually exclusive and opposite hypothesis can be formulated: null hypothesis and alternative hypothesis.

Types of Error in a Hypothesis Test

• In a hypothesis testing, there is always a risk of committing two types of errors.
• The following table summarizes the decisions the researcher could make and the possible consequences

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Acceptance Region (AR) versus Rejection Region (RR)

Acceptance Region versus Rejection Region (cont…)

Steps to conduct a hypothesis test

One-Sample Mean Test

Problems on One-Sample Mean Test

Problems on One-Sample Mean Test (Cont…)

Problems on One-Sample Mean Test (Cont…)

Problems on One-Sample Mean Test (Cont…)

Problems on One-Sample Mean Test (Cont…)

One-Sample Test of Proportions (Cont…)

One-Sample Test of Proportions

Problems on Proportion Test

Problems on Proportion Test (Cont…)

Problems on Proportion Test (Cont…)

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Problem-2: A recent survey indicated that 65 out of 110 surveyed favored the continued use of daylight savings time in the summer. Can we conclude that majority of the people support continued use of daylight savings time in the summer?

Thank you for your attention!