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. A. Ho: µ = 300; Ha: µ < 300; Rejection Region: z < -1.64 B. Ho: µ = 300; Ha: µ < 300; Rejection Region: t < -2.02 C. Ho: µ = 300; Ha: µ > 300; Rejection Region: z > 1.64 D. Ho: µ = 300; Ha: µ ≠ 300; Rejection Region: z < -1.96 or z > 1.96 E. Ho: µ = 300; Ha: µ ≠ 300; Rejection Region: t < -2.57 or t > 2.57
Added by Arthur C.
Step 1
Step 1: **State the Hypotheses** - Null Hypothesis (H0): µ = 300 (the mean contents of the cola bottles is equal to 300 ml) - Alternative Hypothesis (Ha): µ < 300 (the mean contents of the cola bottles is less than 300 ml) Show more…
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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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10. 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 299.4 297.7 301.0 298.9 300.2 297.0 Do these data provide convincing evidence that the mean amount of cola (μ) in all the bottles filled that day differs from the target value of 300 ml? Carry out an appropriate test to support your answer. Make sure to write the null and alternative hypotheses explicitly and draw your conclusion at the α = 5% level of significance. Show all 5 steps.
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