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Brilliant_brown [7]
3 years ago
10

Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because th

e filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of 3 ml. A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are:299.4 297.7 301.0 298.9 300.2 297.0Is this convincing evidence that the mean contents of cola bottles is less than the advertised300 ml? Test at the 5% significance level.
Mathematics
1 answer:
ira [324]3 years ago
5 0

Answer:

No because there is sufficient statistical evidence to suggest that the mean contents of cola bottles is equal to 300 ml as advertised

Step-by-step explanation:

Here we have the measured contents as

299.4

297.7

301.0

298.9

300.2

297.0

Total = 1794.2

∴ Mean = 299.03

Standard deviation = 1.5

We have

z=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}

Where:

\bar x = Mean of sample = 299.03 ml

μ = Mean of population = 300 ml

σ = Standard deviation of population = 3 ml

n = Sample size = 6

α = 5% = 0.05

We set our null hypothesis as H₀ = 300 ml

Our alternative hypothesis is then Hₐ < 300 ml

Therefore,  z = -0.792

The probability from z table is P = 0.2142

Since the P value, 0.2142 is > than the 5% significance level, 0.05 we accept the null hypothesis that the mean contents of cola bottles is 300 ml.

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