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.
$$
t=
$$

Question

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.
$$
t=
$$

Accepted Answer

∻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.⚹◊What is the formula for calculating the t-test statistic when conducting hypothesis testing on the mean?⍭ Generate me a similar question◊

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