The manufacturer of a certain brand of hot dogs claims that

The manufacturer of a certain brand of hot dogs claims that the mean fat content per hot dog is 20 grams. Suppose the standard deviation of the population of these hot dogs is 1.9 grams. A sample of these hot dogs is tested, and the mean fat content per hot dog of this sample is found to be 20.5 grams. Find the probability that the sample mean is at least 20.5 when the sample size is 35.

Solution

Sample mean = 20.5

Claimed mean = 20

Let confidence level = 95%

S.D = 1.9

n = 35

Since, the population SD is given, we shall use the Z-stat

Ho : Fat content is within the range

Ha : Fat content is excessive

Thus,

Z = (X - mu) / [ SD / sqrt(n) ]

= (20.5 - 20) / [ 1.9 / sqrt(35) ]

= 1.556

Z-Crit value = 1.96

Z-stat calculated < Z-crit

Hence, we fail to reject the nul hypothesis.

Hence, fat content is ot excess of what is stated.

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