Exam 9: Estimation and Confidence Intervals

Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation Residence in Florida want a condominium. The null hypothesis is p = 0.55 and the alternate is p ≠ 0)55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 Families want a condominium. What decision should be made regarding the null hypothesis?

What is the probability of making a Type II error if the null hypothesis is actually true?

i. An alternate hypothesis is a statement about a population parameter that is accepted when the Null hypothesis is rejected. ii. The level of significance is the risk we assume of rejecting the null hypothesis when it is actually True. iii. There is only one level of significance that is applied to all studies involving sampling.

A nationwide survey of college students was conducted and found that students spend two hours Per class hour studying. A professor at your school wants to determine whether the time students Spend at your school is significantly different from the two hours. A random sample of fifteen Statistics students is carried out and the findings indicate an average of 1.75 hours with a standard Deviation of 0.24 hours. Given the following printout, what can you determine?

The average cost of tuition, room and board at community colleges is reported to be $8,500 per Year with a standard deviation of $1,200, but a financial administrator believes that the average cost Is higher. A study conducted using 150 community colleges showed that the average cost per year Is $9,000. Let α = 0.05. Given the z-statistic is 5.1, what is our decision about the average cost?

The printout below refers to the weekly closing stock prices for Air Canada on 20 randomly Selected weeks in 2000. Using a 5% level of significance, can you say that the average Air Canada stock price was different From $19.50?

The printout below refers to the weekly closing stock prices for Air Canada on 20 randomly Selected weeks in 2000. Using a 5% level of significance, can you say that the average Air Canada stock price was less than $19)00?

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.

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 Peaches is examined and 50 are found to be defective. What is the critical value for α = 0.025?

For a null hypothesis, H0: µ = 4,000, if the 1% level of significance is used and the z-test statistic is +6)00, what is our decision regarding the null hypothesis?

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 Peaches is examined and 50 are found to be defective. If α = 0.025, what will be the decision?

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 changed from 200? Test using the .05 significance level.

What is the level of significance?

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. What is the sample standard deviation?

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. Which of the following is the alternate hypothesis?

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of significance. The t-value is calculated to be 5.77. At the 0.01 level of significance, what is your decision?

The mean length of a small counter balance bar is 43 millimeters. There is concern that the Adjustments of the machine producing the bars have changed. Test the claim at the 0.02 level that There has been no change in the mean length. The alternate hypothesis is that there has been a Change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. The mean of the sample is 41.5 and The standard deviation 1.784. Computed t = -2.913. Has there been a statistically significant change In the mean length of the bars?

i. One assumption in testing a hypothesis about a proportion is that the data collected are the result Of counting something. ii. One assumption in testing a hypothesis about a proportion is that an outcome of an experiment Can be classified into two mutually exclusive categories, namely, a success or a failure. iii. A proportion is a fraction, ratio or probability that gives the part of the population or sample that Has a particular trait of interest.

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.

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 Peaches is examined and 50 are found to be defective. What is the sample proportion?