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.