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 sample mean ($\bar{x}$) and the population mean ($\mu$)

step 2

Calculate the sample standard deviation ($s$) and the sample size ($n$)

step 3

Use the formula for the t-test statistic: $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$

step 4

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

step 5

Calculate the t-test statistic: $t = \frac{-1}{(1/10)} = -10$

Answer

$t = -10.00$

Key Concept

t-test statistic calculation

Explanation

The t-test statistic is calculated to determine if there is a significant difference between the sample mean and the population mean. It is computed using the difference between the sample mean and the population mean, divided by the standard error of the mean.

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