the universal baking ic purhases bags of flour which vary somewhat in weight. the bakery wants to determine if the mean weights per bag purchased from two suppliers are different, a) perform a hypothesis test at a 10 percent level if the supllier 1 sample mean is 49.74 punds and the standard deviation is 0.49 pound wheras the supplier 2 sample mean is 50.08 pounds and the standard deviation is 0.50 pound b) whaat is implied by the test
Try a two-sample test.
Hypothesis:
Ho: µ1 = µ2
Ha: µ1 does not equal µ2
This is a two-tailed test because the problem is just asking if there is a difference (no specific direction in the alternate hypothesis).
Find the critical or cutoff value using the appropriate table at .10 level of significance for a two-tailed test.
Substitute the values into the appropriate formula and calculate your test statistic. If your test statistic exceeds the critical value from the table, then the null will be rejected in favor of the alternative hypothesis and µ1 does not equal µ2. If your test statistic does not exceed the critical value from the table, then the null will not be rejected and you cannot conclude a difference.
I hope these few hints will help get you started.
To perform a hypothesis test to determine if the mean weights per bag purchased from two suppliers are different, you can follow these steps:
Step 1: State the Hypotheses
- The null hypothesis (H0): The mean weights per bag purchased from supplier 1 and supplier 2 are equal.
- The alternative hypothesis (Ha): The mean weights per bag purchased from supplier 1 and supplier 2 are different.
Step 2: Set the Significance Level
In this case, the significance level is given as 10 percent, which means the probability of rejecting the null hypothesis when it is true is 10 percent (or alpha = 0.10).
Step 3: Calculate the Test Statistic
For this case, you can use an Independent Samples t-test since you have two samples from different suppliers. The test statistic for an independent t-test is given by:
t = (sample_mean_1 - sample_mean_2) / sqrt((sample_std_1^2 / n1) + (sample_std_2^2 / n2))
where:
- sample_mean_1: the sample mean weight from supplier 1 (49.74 pounds)
- sample_mean_2: the sample mean weight from supplier 2 (50.08 pounds)
- sample_std_1: the sample standard deviation from supplier 1 (0.49 pound)
- sample_std_2: the sample standard deviation from supplier 2 (0.50 pound)
- n1: the sample size from supplier 1
- n2: the sample size from supplier 2
Step 4: Calculate the Degrees of Freedom
The degrees of freedom for an independent t-test can be calculated by the formula:
df = ( (sample_std_1^2/n1 + sample_std_2^2/n2)^2 ) / ( ((sample_std_1^2/n1)^2 / (n1 - 1)) + ((sample_std_2^2/n2)^2 / (n2 - 1)) )
Step 5: Determine the Critical Value
Since we are conducting a two-tailed test (alternative hypothesis is that the means are different), we need to divide the significance level (alpha) by 2 and find the critical t-value with degrees of freedom (df) calculated in Step 4.
Step 6: Compare the Test Statistic with the Critical Value
If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Step 7: State the Conclusion
Based on the comparison, state whether there is enough evidence to reject the null hypothesis, which implies that the mean weights per bag purchased from the two suppliers are different.
Now, let's calculate the test statistic and determine the conclusion:
a) Test Statistic Calculation:
t = (49.74 - 50.08) / sqrt((0.49^2/n1) + (0.50^2/n2))
b) Degrees of Freedom Calculation:
df = ( (0.49^2/n1 + 0.50^2/n2)^2 ) / ( ((0.49^2/n1)^2 / (n1 - 1)) + ((0.50^2/n2)^2 / (n2 - 1)) )
After determining the critical t-value based on the significance level and degrees of freedom, compare it with the calculated test statistic and make the conclusion based on whether the test statistic is greater than the critical value or not.
Note: The values of n1 and n2 (sample sizes) are not provided in the question, so you would need to use the actual sample sizes to perform the calculations.