Question

# Many food products contain small quantities of substances that would give an undesireable taste or smell...

Many food products contain small quantities of substances that would give an undesireable taste or smell if they are present in large amounts. An example is the "off-odors" caused by sulfur compounds in wine. Oenologists (wine experts) have determined the odor threshold, the lowest concentration of a compound that the human nose can detect. For example, the odor threshold for dimethyl sulfide (DMS) is given in the oenology literature as 25 micrograms per liter of wine (µg/l). Untrained noses may be less sensitive, however. Here are the DMS odor thresholds for 10 beginning students of oenology.

33    32    30    23    26    21    43    37    35    31

Assume (this is not realistic) that the standard deviation of the odor threshold for untrained noses is known to be ? = 7 µg/l.

(b)Give a 95% confidence interval for the mean DMS odor threshold among all beginning oenology students. (Round your answers to three decimal places.)

(____________, ______________)

(c)Are you convinced that the mean odor threshold for beginning students is higher than the published threshold, 25 µg/l? Carry out a significance test to justify your answer. (Use ? = 0.05. Round your value for z to two decimal places and round your P-value to four decimal places.)

Z=

P Value=

From data we get n = 10, = 31.1, ? = 7

b) The 95% confidence interval is

( - E , + E )

Where,

c = 0.95,

= 4.339

Hence the 95% confidence interval is given by,

( 31.1 - 4.339 , 31.1 + 4.339 )

( 26.761, 35.439 )

c) Here the hypothesis are

H0: = 25 v/s H1: > 25

The test statistic value is

= 2.76

p value = p ( z > 2.76 ) = 1 - p ( z 2.76 ) = 1 - 0.9971 = 0.0029

Here p value < .

Hence we reject null hypothesis.

Conclusion : There are sufficient evidence that the mean odor threshold for beginning students is higher than the published threshold, 25 µg/l .