Student Instructions: Answer the following There are many products that on their
ID: 3361965 • Letter: S
Question
Student Instructions: Answer the following There are many products that on their label, establish a content of the packaging. Select a brand of cleaning detergent(for example ACE or Tide) In their label, they establish a weight of the amount of detergent in each box. Choose a sample of 8 boxes from the selected company and weight the 8 samples on a scale Collect this information and build a hypothesis test, a confidence interval, a P-value and size of sample (n) by comparing the average weight of the samples with the one on the box label. it determines, through the hypothesis test,if there is any diference in the average weight of the sample boxes with the one that appears in the box. Use an alpha for this 0.01 test What is your conclusion?Explanation / Answer
I have collected a sample of 8 boxes of 500 gms. of cleaning detergent and the weights of the amount of detergents on the scale (in gms) is
495.1657, 504.0231, 502.0444, 492.0875, 491.4256, 498.8726, 492.4009, 504.9307
Null Hypothesis H0: The mean weight of the samples is 500 gms.
Alternative Hypothesis Ha: The mean weight of the samples is not 500 gms.
The mean weight of 8 samples is 497.6188
The standard deviation of 8 samples is 5.5784
The standard error of the mean weight, SE = SD / sqrt(n) = 5.5784 / sqrt(8) = 1.9723
Degree of freedom = n - 1 = 8 - 1 = 7
t value at 99% confidence level (significance level of 0.01) and df = 7 is 3.4995
Margin of error = SE * t = 1.9723 * 3.4995 = 6.9021
95% confidence level of mean weight is
(497.6188 - 6.9021, 497.6188 + 6.9021)
(490.7167, 504.5209)
As, the 95% confidence interval contains the value of 500 gms, there is significant evidence at 95% confidence that the mean weight of the samples is 500 gms.
Test statistic t = (Mean difference - 500)/ SE = (497.6188 - 500) / 1.9723 = -1.2073
P-value for t = -1.2073 and df = 7 is 0.13326
For two tail test, P-value is 2 * 0.13326 = 0.26652
As, P-value is greater than the significance level of 0.01, we fail to reject the null hypothesis and conclude that there is no significant evidence at 0.01 significance level that the mean weight of samples is not 500 gms.