Exam 9: Hypothesis Testing

The manager of a local specialty store is concerned with a possible slowdown in payments by her customers.She measures the rate of payment in terms of the average number of days receivables are outstanding.Generally,the store has maintained an average of 50 days with a standard deviation of 10 days.A random sample of 25 accounts gives an average of 54 days outstanding with a standard deviation of 8 days.Determine the critical value for α = .01 to test the hypotheses,and,using the test statistic,determine if the manager should be concerned.

A(n)_____________ hypothesis is the statement that is being tested.It usually represents the status quo,and it is not rejected unless there is convincing sample evidence that it is false.

We are testing H₀: µ ? 42;versus H_A: µ > 42.When $\bar { Y } = 45$ s = 1.2,and n = 15,at ? = .01 we do not reject the null hypothesis.(Assume that the population from which the sample is selected is normally distributed. )

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.At α = .10,we would not reject H₀.

Based on a random sample of 25 units of product X,the average weight is 102 lbs.and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.The alternative hypothesis can be written as H_A: μ > 100.(Assume the population is normally distributed. )

Determine the p-value for H₀: p ≤ .5;versus H_A: p > .5,when n = 225 and $\hat { p } = .54$

If a one-sided null hypothesis for a single mean cannot be rejected at a given significance level,then the corresponding two-sided null hypothesis (i.e. ,the same sample size,the same standard deviation,and the same mean)will ______________ be rejected at the same significance level.

A Type II error is defined as the probability of ________________ H₀,when it should _____________.