Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

The local oil changing business is very busy on Saturday mornings and is considering expanding.A national study of similar businesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6.Suppose the local oil changing business owner,wants to perform a hypothesis test.The null hypothesis is the population mean is 3.6 and the alternative hypothesis is the population mean is not equal to 3.6.The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is 0.05. The decision rule for this problem is to reject the null hypothesis if the observed "t" value 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.Previous studies had indicated that 20% of customers who call the help center are Hispanics whose native language is Spanish and therefore would prefer to talk to a Spanish-speaking representative.This figure coincides with the national proportion,as shown by multiple larger polls.You want to test the hypothesis that 20% of the callers would prefer to talk to a Spanish-speaking representative.You conduct a statistical study with a sample of 35 calls and find out that 11 of the callers would prefer a Spanish-speaking representative.The significance level for this test is 0.01.The value of the test statistic obtained is:

The lifetime of a squirrel follows a normal distribution with mean μ months and a standard deviation $\sigma$ =7 months.To test the alternative hypothesis that μ > 40,25 squirrels are randomly selected.The null hypothesis is rejected when the sample mean is bigger than 43.Assuming that μ=45,the probability of type II error is approximately

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 alternative hypothesis would be _______.

The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.

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 critical "t" values are _______.

When the population standard deviation ( $\sigma$ )is unknown,the value of s - 1 is used to compute the t value.

In many cases a business researcher gathers data to test a hypothesis about a single population mean and the value of the population standard deviation is unknown.In this case the researcher cannot use the z test.

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 delivered per cup is 0.81 ounces,and α = 0.05,the appropriate decision is ________.

The local oil changing business is very busy on Saturday mornings and is considering expanding.A national study of similar businesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6.Suppose the local oil changing business owner,wants to perform a hypothesis test.The null hypothesis is the population mean is 3.6 and the alternative hypothesis that the population mean is not equal to 3.6.The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is _______.

The probability of committing a Type I error is called the power of the test.

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 test would be _______.

The local swim team is considering offering a new semi-private class aimed at entry-level swimmers,but needs a 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 and the alternative hypothesis is "the population mean is greater than 15." If the sample size is 5, $\sigma$ is known,and α = .01,the critical value of z is _______.

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 appropriate decision is _________________.

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 selecting 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 null hypothesis is _________________.

The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.

When a true null hypothesis is rejected,the researcher has made a Type I error.

If a null hypothesis was rejected at the 0.025 level of significance,it will be rejected at a 0.01 level of significance based on the same sample results.

When using the t test to test a hypothesis about a population mean with an unknown population standard deviation ( $\sigma$ )the degrees of freedom is defined as n - 1.

A laptop battery lifespan follows a normal distribution with mean μ = 22 months and a standard deviation $\sigma$ = 6 months.To test the alternative hypothesis that μ < 22 with α = .05,36 laptop batteries are randomly selected.Assuming that μ = 21,the probability of type II error is approximately