Test the Indicated Claim About the Means of Two Populations

question 65

Essay

Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations
are equal. Use the traditional method or P-value method as indicated.
-Two types of flares are tested and their burning times (in minutes) are recorded. The summary statistics are given below.
$$\begin{array} { l } { \text { Brand } X }& { \text { Brand } Y } \\n = 35& n = 40 \\\bar { x } = 19.4 \mathrm {~min} & \bar { x } = 15.1 \mathrm {~min} \\\mathrm {~s} = 1.4 \mathrm {~min} & \mathrm {~s} = 0.8 \mathrm {~min} \\\end{array}$$
Use a 0.05 significance level to test the claim that the two samples are from populations with the same mean. Use the traditional method of hypothesis testing.

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Definitions:

Population Mean

The average value of all the data points in a population, representing the central tendency of the dataset.

Stratified Sampling

A sampling method that divides the population into smaller groups, or strata, based on shared attributes or characteristics before sampling to ensure a more representative sample.

Sampling Method

A technique used in statistics to select a subset of individuals from a population to estimate characteristics of the whole population.

Consumer Products

Goods sold directly to the consumer for personal, family, or household use, as opposed to products intended for industrial or commercial use.