C-2 The Big Brother Eric, has recently bought two packs of reduced (8% Total Fat
ID: 3322924 • Letter: C
Question
C-2 The Big Brother Eric, has recently bought two packs of reduced (8% Total Fat), and original ( 15% Total Fat) biscuits from Joules. As a chemist has decided to investigate the information on each label, as fallow 1) Dose based on 20 biscuits: 2) Content of fat per dose: (2 points) (2 points) (2 points) How he will prove that the information provided by manufacturer is correct? 3) Percent of total fat: Describe briefly each step using the following data Reduced 8% Average Weight: 1.655 g Sample used in each test: 1.210 g Original 15% 1.886 g 1.325 gExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Reduced> Original
Alternative hypothesis: Reduced < Original
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees offreedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.40123
DF = 38
t = [ (x1 - x2) - d ] / SE
t = - 0.58
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of - 0.58. We use the t Distribution Calculator to find P(t < - 0.58)
Therefore, the P-value in this analysis is 0.56.
Interpret results. Since the P-value (0.56) is greater than the significance level (0.05), we cannot reject the null hypothesis.
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