A manufacturer of carbonated drink products produces and sells drinks. The manufacturer takes an observation to determine the sugar content of the drink before and after the addition of the colouring. The results of ten carbonated drinks are as follows. Before 0.50 After 0.79 0.58 0.71 0.75 1.22 0.79 1.17 1.14 0.73 0.90 1.25 0.74 0.80 0.82 0.72 0.82 0.77 0.72 0.91 Assume that the sugar content is normally distributed. a) Find the mean and standard deviation for the difference between sugar content before and after the addition of the colouring. b) At 5% level of significance, test if there is a significant difference between the mean of sugar content before and after the addition of the colouring. c) Construct a 95% confidence interval for the mean difference in sugar content before and after the addition of the colouring. Interpret the interval obtained.

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A manufacturer of carbonated drink products produces and sells drinks. The manufacturer
takes an observation to determine the sugar content of the drink before and after the
addition of the colouring. The results of ten carbonated drinks are as follows.
Before 0.50
0.79
After
1.22
0.80
0.58
0.71
0.90
1.17
1.14
0.73
1.25
0.75
0.74
0.82
0.82
0.77
0.72
0.79
0.72
0.91
Assume that the sugar content is normally distributed.
a) Find the mean and standard deviation for the difference between sugar content before
and after the addition of the colouring.
b) At 5% level of significance, test if there is a significant difference between the mean of
sugar content before and after the addition of the colouring.
c) Construct a 95% confidence interval for the mean difference in sugar content before and
after the addition of the colouring. Interpret the interval obtained.
Transcribed Image Text:A manufacturer of carbonated drink products produces and sells drinks. The manufacturer takes an observation to determine the sugar content of the drink before and after the addition of the colouring. The results of ten carbonated drinks are as follows. Before 0.50 0.79 After 1.22 0.80 0.58 0.71 0.90 1.17 1.14 0.73 1.25 0.75 0.74 0.82 0.82 0.77 0.72 0.79 0.72 0.91 Assume that the sugar content is normally distributed. a) Find the mean and standard deviation for the difference between sugar content before and after the addition of the colouring. b) At 5% level of significance, test if there is a significant difference between the mean of sugar content before and after the addition of the colouring. c) Construct a 95% confidence interval for the mean difference in sugar content before and after the addition of the colouring. Interpret the interval obtained.
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