# The produce manager of a grocery store claims granny smith apples weight a mean of four ounces. The sample size is 10 apples (1,6,22,35,39,53,62,64,66,77) the alpha value will be 0.05.

## What is your question?

Just looking at the data, assuming that the values are in ounces, the sample mean will be significantly greater than the 4 oz.

## To determine whether the claim made by the produce manager is statistically significant, we can perform a hypothesis test.

Step 1: State the null and alternative hypotheses.

- Null hypothesis (H0): The mean weight of granny smith apples is equal to four ounces.

- Alternative hypothesis (Ha): The mean weight of granny smith apples is not equal to four ounces.

Step 2: Select a significance level (alpha value).

The alpha value of 0.05 has already been given, which means we are willing to accept a 5% chance of observing a significant result due to random variation.

Step 3: Collect sample data and calculate the sample mean and standard deviation.

Given the sample size and weights of the 10 apples: 1, 6, 22, 35, 39, 53, 62, 64, 66, 77.

- Sample mean (x̄): (1 + 6 + 22 + 35 + 39 + 53 + 62 + 64 + 66 + 77)/10 = 425/10 = 42.5 ounces.

- Sample standard deviation (s): √[Σ(xi - x̄)^2 / (n - 1)] = √[(1-42.5)^2 + (6-42.5)^2 + ... + (77-42.5)^2] / (10-1).

Step 4: Calculate the test statistic.

The test statistic (t) is calculated as t = (x̄ - μ) / (s / √n), where μ is the hypothesized mean (4 ounces) and n is the sample size (10).

t = (42.5 - 4) / (s / √10)

Step 5: Determine the critical value and p-value.

Based on the given alpha value of 0.05 and the degrees of freedom (n-1 = 10-1 = 9), we can use a t-distribution table or a statistical calculator to find the critical value and p-value.

Step 6: Make a decision.

- If the test statistic falls outside the critical region, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

- If the test statistic falls within the critical region, we fail to reject the null hypothesis and do not have enough evidence to support the alternative hypothesis.

NOTE: Since the standard deviation (s) is not given, it is not possible to calculate the exact test statistic, critical value, and p-value.