Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

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 __________.

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

A car manufacturer looks at past sales and realizes that the most common car color is silver with 24% of purchasers selecting that color.The dealerships in one state believe that car purchasers in their area believe that the proportion of purchasers selecting silver is greater than 24%.Based on a survey of 84 car purchasers in the state, the dealerships find that 26% of them would select silver.If the true proportion selecting silver is 27%, what is the probability of the dealerships making a Type II error, given an alpha of 0.05?

Which of the following best describes the power?

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.

A laptop battery lifespan follows a normal distribution with mean μ = 20 months and a standard deviation $\sigma$ = 6 months.To test the alternative hypothesis that μ > 20 with α = .05, 36 laptop batteries are randomly selected.Assuming that μ = 21, the probability of type II error is approximately ________.

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 power is approximately ________.

A small restaurant owner believes exactly 36 % of his customers come to the restaurant because of his daily half-price specials.He is interested in expanding his daily specials and increasing the price.However, he would like to test his hypothesis prior to expanding the daily special offerings.He intends to use the following null and alternative hypotheses. H_o: p = 0.36 H_a: p $\neq$ 0.36 These hypotheses _______________.

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 in a two-tailed test is +1.96.The observed z value from sample data is -2.11.The decision made by the researcher based on this information is to _____ the null hypothesis.

Whenever hypotheses are established such that the alternative hypothesis is "μ>8", where μ is the population mean, the hypothesis test would be a two-tailed test.

David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks.Based on a recent census of personnel, David knows that the variance of teller training time in the southeast region is 8, and he wonders if the variance in the southwest region is the same number.His staff randomly selected personnel files for 15 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours.Assume that teller training time is normally distributed.Using $\alpha$ = 0.10, the observed value of chi-square 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 _________________.

A business is testing a new product that in reality would make the company money.Based on market research data, the business analyst committed a Type II error by rejecting the null.

In a two-tailed hypothesis about a population mean with a sample size of 100, $\sigma$ is known, and α = 0.10, the rejection region would be _______.

Which if the following would result in a higher probability of making a Type II error?

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 _______.

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

The executives of CareFree Insurance, Inc.feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance.Eighty employees rate the management as participatory.The null hypothesis is __________.

Consider the following null and alternative hypotheses. H_o: $\mu$ $\ge$ 67 H_a: $\mu$ < 67 These hypotheses _______________.

A small restaurant owner believes no more than 36% of his customers travel over 10 miles to his business.He is interested in expanding his customer base through marketing.However, he would like to test his hypothesis prior to investing money in a marketing initiative.He intends to use the following null and alternative hypotheses. H_o: p $\le$ 0.36 H_a: p > 0.36 These hypotheses _______________.