11. Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because the 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: 299.4 297.7 301.0 298.9 300.2 297.0 Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300 ml? Test at the 5% significance level.
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State the null hypothesis (H0) and the alternative hypothesis (H1). H0: μ = 300 ml (the mean contents of cola bottles is equal to 300 ml) H1: μ < 300 ml (the mean contents of cola bottles is less than 300 ml) Show more…
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Filling cola bottles Bottles of a popular cola are supposed to contain 300 milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day’s production. The results are 299.4$\quad 297.7 \quad 301.0 \quad 298.9 \quad 300.2 \quad 297.0$ Do these data provide convincing evidence that the mean amount of cola in all the bottles filled that day differs from the target value of 300 $\mathrm{ml}$ ? Carry out an appropriate test to support your answer.
Testing a Claim
Tests about a Population Mean
Aishwarya K.
Bottles of a popular cola contain, on average, 300 milliliters (ml) of cola. The standard deviation is 3 ml. Assume that the distribution of the contents of the bottles is approximately normal. (a) What percent of the bottles contain more than 305 ml of cola? (b) What percent of the bottles contain between 297 and 301.5 ml of cola? (c) Fill in the blank: Bottles with less than ___ ml of cola fall in the bottom 25% of the distribution.
Chris M.
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