Respuesta :
Answer:
No, there is no evidence that the manufacturer has a problem with underfilled or overfilled bottles, due that according our results we cannot reject the null hypothesis.
Explanation:
according to this exercise we have the following:
σ^2 =< 0.01 (null hypothesis)
σ^2 > 0.01 (alternative hypothesis)
To solve we can use the chi-square statistical test. To reject or not the hypothesis, we have that the rejection region X^2 > 30.14
Thus:
X^2 = ((n-1) * s^2)/σ^2 = ((20-1)*0.0153)/0.01 = 29.1
Since 29.1 < 30.14, we cannot reject the null hypothesis.
An automated filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of S² = 0.0153 (fluid ounces)². If the variance of fill volume exceeds 0.01 (fluid ounces)², an unacceptable proportion of bottles will be underfilled or overfilled. Is there evidence in the sample data to suggest that the manufacturer has a problem with under filled or overfilled bottles? Use α = 0.05, and assume that fill volume has a normal distribution
Answer:
This implies that there is no problems in incorrectly filled because there weren't strong to sustain the there is a problem
Explanation:
Using hypothesis test can come in handy for to measure and accept the real variance and standard deviation of a population distribution
Following the eight steps procedure would guide;
1. Identify the parameter of interest is the population : Variance denoted as S²
2. Formulate the Null hypothesis
H° ;S² = 0.01
3. Draw an alternate hypothesis H¹: S² > 0.01
4.α = 0.05
5. Use Chi ² Test.
The test statistic is:
