Question

Math

Posted 6 months ago

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Jumbo eggs in Australia, on average, are supposed to weigh 68 g. Margot is in charge of a quality control test that involves weighing a sample of eggs to see if the sample mean weight is significantly different than $68 \mathrm{~g}$. She takes a random sample of 100 eggs and finds a mean weight of $67 \mathrm{~g}$ and a sample standard deviation of $1 \mathrm{~g}$.
Margot wants to use these sample data to conduct a $t$ test on the mean. Assume that all conditions for inference have been met.
Calculate the test statistic for Margot's test.
You may round your answer to two decimal places.
$t=$
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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

Calculate the test statistic using the formula $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size

step 2

Substitute the given values into the formula: $t = \frac{67 - 68}{(1/\sqrt{100})}$

step 3

Simplify the denominator: $t = \frac{67 - 68}{(1/10)}$

step 4

Calculate the test statistic: $t = \frac{-1}{0.1} = -10$

step 5

Round the test statistic to two decimal places: $t = -10.00$

Answer

$t = -10.00$

Key Concept

Calculating a t-test statistic

Explanation

The t-test statistic measures how far the sample mean is from the population mean in terms of the standard error. It is used in hypothesis testing to determine if there is a significant difference between the sample mean and the population mean.

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