Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

Discrete Components,Inc.manufactures a line of electrical resistors. Presently,the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically,the quality control inspectors check for conformity by randomly select 10 resistors from the line,and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using $\alpha$ = 0.05,the critical value of chi-square is _________________.

Albert Miller,VP of production of a company that produces components for auto braking systems is examining the diameter of a specialized electrical wire produced with newly acquired machines in a new production line.For safety reasons,it is important that the variance in the diameter doesn't exceed 0.15 inches.Albert knows that the variance of the other production lines is 0.15 and he wants to make sure the new machine also delivers products whose variance doesn't exceed the safety limit.His staff randomly selects a sample of 25 wires and find out that the standard deviation of the sample is 0.42 inches.Assume that wire diameters are normally distributed.Using $\alpha$ = 0.10,the appropriate decision is ________.

The local swim team is considering offering a new semi-private class aimed at entry-level swimmers,but needs at minimum number of swimmers to sign up in order to be cost effective.Last year's data showed that during 8 swim sessions the average number of entry-level swimmers attending was 15.Suppose the instructor wants to conduct a hypothesis test.The alternative hypothesis for this hypothesis test is: "the population mean is less than 15".The sample size is 8, $\sigma$ is known,and α =.05,the critical value of z is _______.

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8,a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The table "t" value for this problem is _______.

If the p-value for a one-tailed test is 0.019,then the null hypothesis

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief,a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchased this company's brand of the product.If a researcher wants to conduct a statistical test for this problem,the observed z value would be _______.

Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday,the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using $\alpha$ = 0.10,the appropriate decision is _______.

The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Your company claims that the average waiting time is 7 minutes at the busiest time,from 8 a.m.to 10 a.m.,Monday through Thursday.One of your main clients has recently complained that every time she calls during the busy hours,the waiting time exceeds 7 minutes.You conduct a statistical study to determine the average waiting time with a sample of 35 calls,for which you obtain an average waiting time of 8.15 minutes.Suppose that you can assume that waiting times are normally distributed.The sample standard deviation is 4.2 minutes.The null hypothesis is:

A recent survey suggests 30% of boat owners do not regularly use their boat after the second year of ownership.A local boat dealer wants to test the alternative hypothesis that p ≠ .30 with α = .05.He surveys 60 boat owners and finds 42% of the owners who have owned their boat for three years report they do not regularly use their boat.Assuming that p = .35,the probability of type II error is approximately

A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup,but a consumer believes that the actual mean amount is less.The consumer obtained a sample of 49 cups of the dispensed liquid with average of 7.75 ounces.If the sample variance of the dispensed liquid per cup is 0.81 ounces,and α = 0.05,the p-value is approximately

A z test of proportions is used when a hypothesis test is conducted on a population proportion.

The weight of a USB flash drive is 30 grams and is normally distributed. Periodically,quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise,the production process continues.The last sample showed a mean and standard deviation of 31.9 and 1.8 grams,respectively. Using $\alpha$ = 0.10,the appropriate decision is _______.

If a null hypothesis was not rejected at the 0.10 level of significance,it will be rejected at a 0.05 level of significance based on the same sample results.

Consider the following null and alternative hypotheses. These hypotheses _______________.

The probability of committing a Type II error changes for each alternative value of the parameter.

When a researcher fails to reject a false null hypothesis,a Type II error has been committed.

Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday,the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using $\alpha$ = 0.10,the critical z value is _______.

Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday,the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 38 defaulted loans. Using $\alpha$ = 0.10,the appropriate decision is _______.

In testing a hypothesis about a population mean with an unknown population standard deviation ( $\sigma$ )the degrees of freedom is used in the denominator of the test statistic.

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8,a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______.