The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean

Question

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The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean

weight of 3.8 ounces with a sample standard deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is less than 4 ounces. The correct calculated value of the test statistic is _______.

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-02-28T04:31:19+03:00

Answer:

$t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549$

Step-by-step explanation:

Given data and notation

$\bar X=3.8$ indicates the sample mean

$s=0.5$ refers to the sample standard deviation

$n=15$ is the sample size

$\mu_o =4$ represents the value we are testing.

$\alpha$ indicates the significance level for the hypothesis test.

t refers to the statistic of interest.

$p_v$ is the p-value for the test (the variable we are interested in).

Formulate the null and alternative hypotheses.

I will set up the hypotheses to verify if the mean weight falls below 4 ounces, formalizing:

Null hypothesis: $\mu \geq 68$

Alternative hypothesis: $\mu < 4$

Since our sample size is < 30 and the population standard deviation is unknown, it’s advisable to utilize a t test to compare the actual mean against the reference value, with the statistic calculated as follows:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "This test compares group means and is commonly utilized to determine if the mean is (greater than, less than, or not equal to) a specific value."

Calculate the statistic

We can substitute the provided information into formula (1):

$t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549$