1. A researcher believes that the average size of farms in the U.S. has increase
ID: 1202567 • Letter: 1
Question
1. A researcher believes that the average size of farms in the U.S. has increased from the 2002 mean of 471 acres. She took a sample of 23 farms in 2011 to test her belief and found a sample mean of 487 acres and a sample standard deviation of 46.9 acres. At a 5% level of significance, test the researcher's claim. What is your conclusion?
2. A study by Hewitt Associates showed that 79% of companies offer employees flexible scheduling. Suppose a researcher believes that in accounting firms this figure is lower. The researcher randomly selects 410 accounting firms and determines that 304 of these firms have flexible scheduling. At a 1% level of significance, does your test show enough evidence to conclude that a significantly lower percentage of accounting firms offer employees flexible scheduling? What is the p-value for this test?
3. The American Lighting Company developed a new light bulb that it believes will last at least 700 hours on average. A test is to be conducted using a random sample of 50 bulbs, and a 1% level of significance. Assume that the population standard deviation is 10 hours. What are the consequences of making a type II error? What is the probability of making a Type II error if the true population mean is 695 hours?
Explanation / Answer
Answer:
Given the information:
A researcher believes the average size of farms mean increases to 471 acres from the 2002.
That is: X = 471
She took a sample of 23 farms in 2011 to test her belief and found a sample mean of 487 acres.
That is: n = 23
The standard deviation (SD) of the sample is: 46.9 acres.
Level of significance (Los) is at: 5% (or) 0.05
Null Hypothesis (H0) for this test is: H0 = 471
Alternative Hypothesis (Ha) for this test is: Ha = 471
In this case, the sample size (23) is less than 30. So we can use small sample test. By using the t-distribution, we get the test statistic at the level of significance 5%, the P value is: 1.636. That is: t22 = 1.636.
Therefore, the P-value fail to reject the null hypothesis. Therefore, at 0.05 level of significance data provides not enough evidence to support the researcher's belief that the average size of farms in the U.S. has increased from the 2002 mean of 471 acres.
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