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NISA [10]
3 years ago
12

Factory produces 1000 bottles of Hosta sauce in a day. 50 bottles are selected at random to determine whether they were the corr

ect amount. The factory Jack's bottles that are over under the correct weight.
One bottle is underweight, 46 bottles are the correct weight, and 3 bottles are overweight.

Based on this random sample, approximately how many bottles will the factory widget from the days production?
Mathematics
1 answer:
BabaBlast [244]3 years ago
6 0
<span>Based on this sample, and assuming the word "widget" means removed, the answer is four. They only tested 50 bottles and found four (one under, three over). The question also contains the word "Jack's, " the meaning is unclear. The factory shipped 1000 bottles of Hosta sauce, assuming the same ratio as the random sample (0.0008%) then the factory shipped 80 bottles that are incorrect.</span>
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Answer:

The 80% confidence interval for the the population mean nitrate concentration is (0.144, 0.186).

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We have to calculate a 80% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=0.165.

The sample size is N=25.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.078}{\sqrt{25}}=\dfrac{0.078}{5}=0.016

The degrees of freedom for this sample size are:

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The t-value for a 80% confidence interval and 24 degrees of freedom is t=1.318.

The margin of error (MOE) can be calculated as:

MOE=t\cdot s_M=1.318 \cdot 0.016=0.021

Then, the lower and upper bounds of the confidence interval are:

LL=M-t \cdot s_M = 0.165-0.021=0.144\\\\UL=M+t \cdot s_M = 0.165+0.021=0.186

The 80% confidence interval for the population mean nitrate concentration is (0.144, 0.186).

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