A company sells cans of caviar that say they each contain 100g. of product with a standard deviation of 1g. A consumer advocacy group suspects that the company 13 under-filling these cans. The group obtains a simple random sample of 30 cans and measures how much product is In each can. They calculate a sample mean of 99g. They will take further action if this ls significantly lower than the advertised amount. Find the P-value.

Question

Mathematics

Chase Gibbs

1 July, 08:32

A company sells cans of caviar that say they each contain 100g. of product with a standard deviation of 1g. A consumer advocacy group suspects that the company 13 under-filling these cans. The group obtains a simple random sample of 30 cans and measures how much product is In each can. They calculate a sample mean of 99g. They will take further action if this ls significantly lower than the advertised amount. Find the P-value.

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Deangelo Christensen · Answer 1

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 100g

For the alternative hypothesis,

µ < 100g

Due to the <, It means that it is left tailed test.

Since the number of samples is large, the population standard deviation is given, the z test would be used. The formula is

z = (x - µ) / (σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 100g

x = 99 g

σ = 1g

n = 30

z = (99 - 100) / (1/√30) = - 5.48

Looking at the normal distribution table, the probability corresponding to the z score is less than 0.00001

P value < 0.00001