Exam 7: Confidence Intervals

The manager of a grocery store wants to determine whether the amount of water contained in a 1L bottle purchased from a known manufacturer actually averages to 1L. It is known from the manufacturer's specifications that the standard deviation of the amount of water is equal to 0.02L. A random sample of 32 bottles is selected, and the mean amount of water per 1L bottle is found to be 0.995L. -The test statistic is _____.

A new manufacturing method has been introduced to streamline the canning process of cherries. Although the time to fill a can has been reduced, the quality control manager is concerned about the uniformity of the amount of cherries in each can. The cans are labelled to contain 14.5 grams of cherries (the remaining volume consisting of natural juice). To be sure that this level has not been affected by the new canning method, the manager randomly samples 80 cans over an eight hour shift. The mean number of grams is 14.64. The population standard deviation is known to be 0.4g. -The null and alternative hypothesis to determine if the new method has changed the amount of cherries that should be in the can is _____.

In a two-sided hypothesis test,if the p-value is less than $\alpha$ ,then

Setup the null and alternative hypothesis that will test the claim that the percentage of women preferring white wine is 25% higher than men.

A survey of the wine market has shown that the preferred wine for 17% of those surveyed is merlot. A merlot wine producer believes the figure is higher. A random sample of 550 adults was asked which wine they preferred. Suppose 115 replied that merlot was their wine preference. -The appropriate test statistic to test the hypotheses is _____.

The power of a statistical test is the probability of ______________ the null hypothesis when it is ________.

A new company is in the process of evaluating its customer service.The company offers two types of sales: 1.Internet sales;2.Store sales.The marketing research manager believes that the Internet sales are more than 10% higher than store sales.The alternative hypothesis for this problem would be stated as:

In testing the difference between the means of two normally distributed populations with known population standard deviations,we can only use a two-sided test.

Failure to meet payments on student loans has been a major problem for both banks and the government. Approximately 50% of all student loans are in default. A random sample of 350 loans to students indicates that 147 are in default. -How much evidence do we have that the percentage of students loans in default is not 50%?

When conducting a hypothesis test about a population mean at a given level of significance,as the sample size n increases the power of the test _____.

A researcher wishes to test H₀: $\mu$ = 50 versus H_a: $\mu$ > 50.A sample of size n = 25 is take from a normally distributed population with mean $\mu$ = 55 and standard deviation is $\sigma$ = 10.What is the probability of a Type II error at the 5% level of significance?

A sample of 400 journalism majors at a research university were asked if they agreed with the following statement "Government should be more involved in oversight and regulation of reporting". Fifty-two (52) percent of the respondents agreed with the statement. -The p-value associated with the test statistic is _____.

When carrying out a test of H₀: p = .4 versus H_a: p < .4 and z is the calculated test statistic,we reject H₀ at level of significance $\alpha$ When:

The ______________ is the probability,computed assuming that the null hypothesis H₀ is true,of observing a value of the test statistic that is at least as contradictory to H₀ and supportive of H_a as the value actually computed from the sample data.

In an opinion survey, a random sample of 1000 adults from the USA and 1000 adults from Germany were asked whether they supported the death penalty. 590 American adults and 560 German adults indicated that they supported the death penalty. The researcher wants to know if there is sufficient evidence to conclude that the proportion of adults who support the death penalty is higher in the USA than in Germany. -Write the null hypothesis.

A marketing research company surveyed grocery shoppers in the east and west coasts to see the percentage of the customers who prefer chicken to other meat.The data are given below. Sample size Number of customers in the sample that prefer chicken East Coast 492 156 West Coast 386 172 -Is the proportion of customers who prefer chicken the same for the two regions? Test at

At the 5% level of significance,test H₀: p = 0.2 versus H_a: p

What is the estimated value of p₂?

Calculate the test statistic and test the claim at

When testing the difference between two population proportions using large,independent random samples,the appropriate test statistic is based on the ____ distribution.