Define the following: Type I Error, Type II Error, Null Hypothesis, Alternate Hy

Question

Define the following: Type I Error, Type II Error, Null Hypothesis, Alternate Hypothesis. Alpha (a), Significance Level. Critical Value, Rejection Region. Test Statistic, and p-value Coca-Cola tested a sample to see if they are averaging 12 ounces as stated on their cans. The test provided evidence suggesting that the cans were not 12 ounces on average. Before spending large amounts of resources to adjust production, management decided to conduct several more tests with larger samples. The new tests demonstrated that the cans were in fact still averaging 12 ounces. Identify and explain the type of error that happened in the first round of testing. Previously, the U.S. Census reported that the average family consists of 3.14 persons with a standard deviation of 137 persons. In order to find out if the average has changed from the previous results, a sample of 5.000 families was collected with an average of 3.10 persons. The U.S. Census wants to be ninety-eight percent confident when they report if the average is now lower or if there has not been any significant change. a. Write the Null and Alternate Hypothesis b. What is alpha (a) in this scenario? c. Would you conduct a 1 -tailed test (upper or lower) or a 2-tailed test? d. What critical value will you use to identify the rejection regions? e. Write the test statistic formula you should use f. Calculate the test statistic g. State your conclusion - Reject or fail to reject the null hypothesis h. What should the U.S. Census report per the results of this test? i. What is the p-value? j. To what should you compare the p-value to make a conclusion on this hypothesis test? k. What's your conclusion based on the p-value and how did you decide? A group of scientists wanted to compare the intelligence of the Sus Scrofa Domesticus (SSD) and the Canis Lupus Familiaris (CLF). After a series of tests, they gathered the average scores of a sample of 15 SSD and 16 CLF. The SSD average intelligence score was 60 points (variance of 36 points) and an average intelligence score of 56 points (variance of 25 points) for the CLF. The scientists want to know with a ninety percent certainty if these two animals have different intelligence levels. a. Write the Null and Alternate Hypothesis b. What is alpha (a) in this scenario? c. Would you conduct a 1-tailed test (upper or lower) or a 2-tailed test? d. Calculate the degrees of freedom for this test e. What critical value will you use to identify the rejection regions? f. Calculate the pooled variance for these samples g. Write the test statistic formula you should use h. Calculate the test statistic i. State your conclusion - Reject or fail to reject the null hypothesis j. What should the scientists report per the results of this test?

Explanation / Answer

1)

a) Type-I error: Rejecting the null hypothesis (Ho) when the null hypothesis is true is called an error of type-I

b) Type-II error: Accepting the null hypothesis (Ho) when the null hypothesis is false is called an error of type-II

c) Null hyppothesis: The assumption of no difference is called null hypothesis and it is denoted by Ho.

d) Alternative hypothesis: The complete opposite statement of null hypothesis is called alternative hypothesis and it is denoted by H1 or Ha.

e) Level of significance: Probability of type one error is called level of significance and it is denoted by alpha

i.e. alpha = P{Rejecting Ho/Ho is true}

f) Critical value&Rejection region: It is the value which is obtained by the tests based on the certain distribution . It is used in testing of hypothesis.

A critical value is a line on a graph that splits the graph into sections. One or two of the sections is the “rejection region”; if your test value falls into that region, then you reject the null hypothesis. A one tailed test with the rejection rejection in one tail.

g) Test statistic: A test statistic is a standardized value that is calculated from sample data during a hypothesis test. You can use test statistics to determine whether to reject the null hypothesis. The test statistic compares your data with what is expected under the null hypothesis.

h) P Value: It is the probability of observed difference and it is also defined as p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected.

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