A certain band of apple juice is supposed to have 64 ounces
of juice. The company's target mean is 64.05 ounces of juice
to avoid penalties for underfilling. The quality control manager
wishes to verify that the mean amount of juice being dispensed
really is 64.05 ounces. She randomly selects 22 bottles and
obtains the data below.
Use an alpha of 0.01.
To determine whether the mean amount of juice being dispensed is really 64.05 ounces, we can conduct a hypothesis test using the given data. Here's how to do it:
Step 1: State the hypotheses:
- Null hypothesis (H₀): The mean amount of juice dispensed is equal to 64.05 ounces.
- Alternative hypothesis (Hₐ): The mean amount of juice dispensed is not equal to 64.05 ounces.
Step 2: Determine the significance level (alpha):
The significance level, also known as alpha (α), is given in the question as 0.01.
Step 3: Calculate the test statistic:
We'll use the t-test statistic since the sample size is small (< 30) and the population standard deviation is unknown.
The formula to calculate the t-test statistic for a single sample is: t = (sample mean - population mean) / (sample standard deviation / √n)
Step 4: Define the rejection region:
For a two-tailed test at a significance level of 0.01, we need to divide alpha by 2, resulting in an alpha/2 of 0.005. We can use a t-distribution table or a statistical calculator to find the critical t-value for a given alpha/2 and degrees of freedom (n-1). In this case, degrees of freedom is 22 - 1 = 21.
Step 5: Make a decision:
Compare the calculated test statistic to the critical t-value to make a decision.
If the test statistic falls within the rejection region (beyond the critical t-values), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
As the data necessary to perform the calculations is not mentioned in the question, please provide the data (amount of juice in the 22 bottles) to continue the calculation process.