the average 1-ounce chocolate chip cookie contains 110 calories. A random sample of 15 different brands of 1-ounce chocolate chip cookies results in the following calorie amounts, at the a = 0.01 level, is there sufficient evidence that the average calories contents is greater than 110 calories
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To determine if there is sufficient evidence that the average calorie content of 1-ounce chocolate chip cookies is greater than 110 calories, we can perform a hypothesis test. The null and alternative hypotheses for this test can be stated as follows:
Null hypothesis (H0): The average calorie content of 1-ounce chocolate chip cookies is not greater than 110 calories.
Alternative hypothesis (Ha): The average calorie content of 1-ounce chocolate chip cookies is greater than 110 calories.
To conduct the hypothesis test, we can follow these steps:
Step 1: Set up the hypotheses.
H0: µ ≤ 110 (The population mean calorie content is less than or equal to 110)
Ha: µ > 110 (The population mean calorie content is greater than 110)
Step 2: Select a significance level (α).
In this case, the significance level is given as α = 0.01.
Step 3: Collect sample data.
The sample data provided is as follows:
(Provide the calorie amounts of the 15 different brands of 1-ounce chocolate chip cookies)
Step 4: Compute the test statistic.
We will use the t-test statistic, which is suitable for small sample sizes when the population standard deviation is unknown. The formula for calculating the t-test statistic is as follows:
t = (x̄ - µ) / (s / √n)
where:
x̄ is the sample mean,
µ is the hypothesized population mean,
s is the sample standard deviation,
n is the sample size.
Step 5: Calculate the p-value.
Using the test statistic calculated in the previous step, we can look up the corresponding p-value in the t-distribution table or use statistical software to find the p-value directly.
Step 6: Make a decision.
Compare the p-value to the significance level α. If the p-value is less than α, we reject the null hypothesis (H0) and conclude that there is sufficient evidence to support the alternative hypothesis (Ha). Otherwise, if the p-value is greater than or equal to α, we fail to reject the null hypothesis (H0).
Please provide the sample data (calorie amounts) so we can continue with the calculations.
To determine if there is sufficient evidence that the average calorie content of the 1-ounce chocolate chip cookies is greater than 110 calories, we will perform a hypothesis test using the given sample data. Here are the steps to follow:
Step 1: State the hypotheses:
- Null hypothesis (H₀): The average calorie content of the 1-ounce chocolate chip cookies is not greater than 110 calories (μ ≤ 110).
- Alternative hypothesis (H₁): The average calorie content of the 1-ounce chocolate chip cookies is greater than 110 calories (μ > 110).
Step 2: Choose the significance level.
In this case, the given significance level is α = 0.01. This represents the probability of making a Type I error, which is rejecting the null hypothesis when it is true.
Step 3: Collect and calculate the sample data.
The given sample data contains the calorie amounts for 15 different brands of 1-ounce chocolate chip cookies.
Step 4: Compute the test statistic.
We will calculate the test statistic based on the sample data. In this case, since the population standard deviation is not provided, we will use a t-test for the sample mean.
Step 5: Determine the critical value.
We need to determine the critical value based on the significance level and the degrees of freedom, which is calculated as the sample size minus 1. In this case, since the alternative hypothesis is for a greater value, we will use a one-tailed test.
Step 6: Compare the test statistic with the critical value.
If the test statistic value exceeds the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Step 7: Calculate the p-value.
If the test statistic value exceeds the critical value, we can also calculate the p-value, which represents the probability of obtaining a test statistic value as extreme as the observed value under the assumption that the null hypothesis is true. If the p-value is less than the significance level, we reject the null hypothesis.
Step 8: Make a decision.
Based on the comparison between the test statistic and the critical value or the p-value and the significance level, we can make a decision to either reject or fail to reject the null hypothesis.
By following these steps, you can analyze the given sample data and determine if there is sufficient evidence to support the claim that the average calorie content of the 1-ounce chocolate chip cookies is greater than 110 calories at the 0.01 significance level.