Exam 9: Estimation and Confidence Intervals

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of Seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8)4, and 6.6 pounds. Does this sample support the original claim? What is the alternate hypothesis?

The Jamestown Steel Company manufactures and assembles desks and other office equipment at Several plants. The weekly production of the Model A325 desk follows a normal probability Distribution, with a mean of 200 and a standard deviation of 16. Recently, due to market expansion, New production methods have been introduced and new employees hired. The vice president of Manufacturing would like to investigate whether there has been a change in the weekly production Of the Model A325 desk. The mean number of desks produced last year (50 weeks, because the Plant was shut down two weeks for vacation) is 203.5. Is the mean number of desks produced Different from 200? Test using the .01 significance level. i. The alternate hypothesis is μ ≤ 200. ii. It is appropriate to use the z-test. iii. The decision rule is: if the computed value of the test statistic is not between -2.58 and 2.58, Reject the null hypothesis.

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the Population mean is not equal to 16.9. A random sample of 16 items results in a sample mean of 18.0 And the sample standard deviation is 2.4. It can be assumed that the population is normally Distributed. Determine the observed "t" value.

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of Seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8)4, and 6.6 pounds. Does this sample support the original claim? The null hypothesis is:

i. To prevent bias, the level of significance is selected before setting up the decision rule and Sampling the population. ii. The level of significance is the probability that a true hypothesis is rejected. iii. If the critical values of the test statistic z are ±1.96, they are the dividing points between the areas Of rejection and non-rejection.

What do tests of proportions require of both np and n(1 - p)?

i. Two types of possible errors always exist when testing hypotheses-a Type I error, in which the Null hypothesis is rejected when it should not have been rejected, and a Type II error in which the Null hypothesis is not rejected when it should have been rejected. ii. A test statistic is a value determined from sample information collected to test the null hypothesis. iii. If we do not reject the null hypothesis based on sample evidence, we have proven beyond doubt That the null hypothesis is true.

What are the critical z-values for a two-tailed hypothesis test if α = 0.01?

i. A sample proportion is found by dividing the number of successes in the sample by the number Sampled. ii. The standard normal distribution is the appropriate distribution when testing a hypothesis about a Population proportion. iii. When testing population proportions, the z statistic can be used when np and n(1 - p) are greater Than five.

i. The probability of a Type I error is also referred to as alpha. ii. A Type I error is the probability of accepting a true null hypothesis. iii. A Type I error is the probability of rejecting a true null hypothesis.

What are the two rejection areas in using a two-tailed test and the 0.01 level of significance when The population standard deviation is known?

A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the Average sponge could absorb 103.5ml. After the redesign, the absorption amounts of a sample of Sponges were (in millilitres): 121.3, 109.2, 97.6, 103.5, 112.4, 115.3, 106.5, 112.4, 118.3, and 115.3. What is The decision rule at the 0.01 level of significance to test if the new design increased the absorption Amount of the sponge?

The claim that "40% of those persons who retired from an industrial job before the age of 60 would Return to work if a suitable job was available" is to be investigated at the 0.02 level of risk. If 74 out Of the 200 workers sampled said they would return to work, what is our decision?

A manufacturer claims that less than 1% of all his products do not meet the minimum government Standards. A survey of 500 products revealed ten did not meet the standard. If the computed value of z = -2.25 and the level of significance is 0.03, what is your decision?

i. To set up a decision rule, the sampling distribution is divided into two regions-a region of non- Rejection and a region where the null hypothesis is rejected. ii. A test statistic is a value determined from sample information collected to test the null hypothesis. iii. If the null hypothesis is true and the researchers do not reject it, then a correct decision has been Made.

i. The standard normal distribution is the appropriate distribution when testing a hypothesis about a Population proportion. ii. When testing population proportions, the z statistic can be used when np and n(1 - p) are greater Than five. iii. To conduct a test of proportions, the assumptions required for the binomial distribution must be met.

A manufacturer claims that less than 1% of all his products do not meet the minimum government Standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is -1.96 and the level of significance is 0.01, what is your decision?

The mean gross annual incomes of certified tack welders are normally distributed with the mean of $50,000 and a standard deviation of $4,000. The ship building association wishes to find out Whether their tack welders earn more or less than $50,000 annually. The alternate hypothesis is That the mean is not $50,000. If the level of significance is 0.10, what is the critical value?

Which of the following is a test statistic used to test a hypothesis about a population?

The Jamestown Steel Company manufactures and assembles desks and other office equipment at Several plants. The weekly production of the Model A325 desk follows a normal probability Distribution, with a mean of 200 and a standard deviation of 16. Recently, due to market expansion, New production methods have been introduced and new employees hired. The vice president of Manufacturing would like to investigate whether there has been a change in the weekly production Of the Model A325 desk. Is the mean number of desks produced different from 200? Test using the )01 significance level. The mean number of desks produced last year (50 weeks, because the plant Was shut down two weeks for vacation) is 203.5. i. The alternate hypothesis is μ ≠ 200. ii. The calculated value of z is 1.55. iii. The decision rule is: if the computed value of the test statistic is not between -2.58 and 2.58, Reject the null hypothesis.