A manufacturer makes ball bearings that are supposed to have a mean weight of 30g. A retailer suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16 ball bearings is 28.8 g with a standard deviation of 3.9 g At the 0.05 significance level test the claim that the sample comes from a population with a mean weight less tan 30g Assume that the weights are normally distributed. Choose an answer for each question
The alternative hypothesis is? A) µ ≠ 30.0 B) µ < 30.0 C) µ ≥30.0 D) µ< 28.8
The type of test is a) left tail b) right tail c) two tail
The test statistic for this hypothesis test is? -1.75 -1.52 -1.97 or -1.23
The critical value for the rejection region is -1.645 -1.753 -1.96 -1.697
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The alternative hypothesis is:
B) µ < 30.0
The type of test is:
A) left tail
The test statistic for this hypothesis test is:
-1.75
The critical value for the rejection region is:
-1.645
The alternative hypothesis is option B) µ < 30.0. In this case, the retailer suspects that the mean weight of the ball bearings is less than 30g.
The type of test is a) left tail. Since the alternative hypothesis is that the mean weight is less than 30g, we are looking for evidence to support this claim in the left tail of the distribution.
The test statistic for this hypothesis test is -1.75. To calculate the test statistic, we use the formula:
test statistic = (sample mean - population mean) / (standard deviation / sqrt(sample size))
= (28.8 - 30) / (3.9 / sqrt(16))
= -1.2 / (3.9 / 4)
= -1.2 / 0.975
= -1.23
The critical value for the rejection region is -1.645. The critical value is obtained from the standard normal distribution table at the 0.05 significance level for a one-tailed test. The critical value divides the area under the curve into the rejection region. In this case, since it's a one-tailed left tail test, we look for the critical value in the left tail of the distribution. The critical value at the 0.05 significance level is -1.645.
Therefore, the answer choices are as follows:
1) The alternative hypothesis is B) µ< 30.0.
2) The type of test is a) left tail.
3) The test statistic for this hypothesis test is -1.23.
4) The critical value for the rejection region is -1.645.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will start you out.
Ha: µ < 30
Z = (score-mean)/SEm
SEm = SD/√n