A food company claims that the average weight of their cereal boxes is 500 grams. To test this claim, a consumer protection agency randomly selects 20 boxes and finds that the average weight of the selected boxes is 495 grams with a standard deviation of 10 grams. Test the company's claim at the 1% level of significance.
Question
A food company claims that the average weight of their cereal boxes is 500 grams. To test this claim, a consumer protection agency randomly selects 20 boxes and finds that the average weight of the selected boxes is 495 grams with a standard deviation of 10 grams. Test the company's claim at the 1% level of significance.
Solution
In this case, since the sample size is less than 30 (n = 20), we should use a t-test instead of a z-test. Here are the steps:
Step 1: State the null and alternative hypotheses. The null hypothesis (H0) is that the mean weight of the cereal boxes is 500 grams. The alternative hypothesis (H1) is that the mean weight is not 500 grams.
H0: μ = 500 H1: μ ≠ 500
Step 2: Calculate the test statistic. The test statistic for a one-sample t-test is calculated as follows:
t = (X̄ - μ0) / (s/√n)
where X̄ is the sample mean, μ0 is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.
t = (495 - 500) / (10/√20) = -2.24
Step 3: Determine the critical value. The critical value for a two-tailed t-test with 19 degrees of freedom (n-1) at the 1% level of significance is approximately ±2.861.
Step 4: Make a decision. Since the absolute value of the test statistic (2.24) is less than the absolute value of the critical value (2.861), we fail to reject the null hypothesis.
Step 5: Interpret the result. There is not sufficient evidence at the 1% level of significance to reject the company's claim that the average weight of their cereal boxes is 500 grams. The data does not provide strong evidence to suggest that the mean weight is different from 500 grams.
Similar Questions
Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 12 boxes. It is reasonable to assume that the population is approximately normal.13.09 14.53 13.18 13.19 13.17 13.0913.12 14.53 13.02 13.01 13.08 13.09Send data to ExcelPart: 0 / 20 of 2 Parts CompletePart 1 of 2Construct a 99% confidence interval for the mean weight. Round the answers to three decimal places. <<μ
The amount of cereal in boxes, packed by a particular machine, is normally distributed with mean µ gram andstandard deviation 5 gram. If the advertised weight of a box is 500 gram, find(i) the proportion of boxes that will be underweight (i.e. weight less than 500 gram) when µ = 505;(ii) the value of µ required to ensure that only 1% of the boxes are underweight.(b) As a check on the setting of the machine a random sample of four boxes is chosen and the setting changed if theaverage weight of the four boxes is less than 500 gram. Find the probability that the setting of the machine ischanged when µ = 505.
Suppose that a candy company packages a bag of jelly beans whose weight is supposed to be 30 grams, but in fact, the weight varies from bag to bag according to a normal distribution with mean μ = 30 grams and standard deviation σ = 3 grams.If the company sells the jelly beans in packs of 9 bags, what can we say about the likelihood that the average weight of the bags in a randomly selected pack is 2 or more grams lighter than advertised? There is about a 2.5% chance of this occurring. It is extremely unlikely for this to occur; the probability is very close to 0. There is about a 5% chance of this occurring. There is no way to evaluate this likelihood, since the sample size (n = 9) is too small. There is about a 16% chance of this occurring.
A random sample of 12 items is taken and is found to have a meanweight of 50 grams and a standard deviation of 9 gramsWhat is the mean weight of population1. with 95% confidence2. with 99% confidence
A random sample of 59 avocados is selected from an orchard and the weight of each avocado is measured. The mean weight is 288.3 grams and the standard deviation is 95.6 grams.Calculate the standard error.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.