Question

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​ _______.

Answer 1

`t=(3.8-4)/((0.5)/(√(15)))=-1.549`

Explanation:

Data given and notation

`\bar X=3.8` represent the sample mean

`s=0.5` represent the sample standard deviation for the sample

`n=15` sample size

`\mu_o =4` represent the value that we want to test

`\alpha` represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

`p_v` represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean weight is less than 4 ounces, the system of hypothesis would be:

Null hypothesis:
`\mu \geq 68`

Alternative hypothesis:
`\mu < 4`

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

`t=(3.8-4)/((0.5)/(√(15)))=-1.549`