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A bottle states that it contains 300ml of water. Olivia measures the amount of water in twenty randomly selected bottles, finding that the mean is 298ml and the estimate of the population standard deviation is 6ml. Test, using a 5% significance level, whether the mean amount of water in a bottle is different from 300ml. You may assume that the amount of water in a bottle is normally distributed.

User Octav
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Final answer:

To test whether the mean amount of water in a bottle is different from 300ml, a one-sample t-test can be used with a significance level of 5%. The null hypothesis is that the mean amount of water is 300ml, and the alternative hypothesis is that it is different. The test statistic can be compared to critical values to determine whether to reject or fail to reject the null hypothesis.

Step-by-step explanation:

This question involves conducting a hypothesis test to determine if the mean amount of water in a bottle differs from 300ml. We can use a one-sample t-test to compare the sample mean (298ml) to the hypothesized population mean (300ml), given that the population standard deviation is estimated to be 6ml. We will use a 5% significance level.

The null hypothesis (H0) is that the mean amount of water in a bottle is equal to 300ml. The alternative hypothesis (H1) is that the mean amount of water in a bottle is different from 300ml.

To test this hypothesis, we can calculate the test statistic using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Once we have the test statistic, we can compare it to the critical values from the t-distribution table with (n-1) degrees of freedom (where n is the sample size). If the test statistic falls within the critical region, we reject the null hypothesis and conclude that the mean amount of water in a bottle is different from 300ml. Otherwise, we fail to reject the null hypothesis.

User Changa
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