Decide in each case whether the hypothesis issimple or composite:(a) the hypothesis that a random variable has a gammadistribution with α = 3 and β = 2;(b) the hypothesis that a random variable has a gammadistribution with α = 3 and β Z 2; (c) the hypothesis that a random variable has an expo-nential density; (d) the hypothesis that a random variable has a beta dis-tribution with the mean μ = 0.50.

The records of a casualty insurance company show that, in the past, its clients have had a mean of  1.8  auto accidents per day with a variance of  0.0016 . The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to  0.0016 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis  H0  and the alternative hypothesis  H1  that we would use for this test. H0 :    H1 :

The records of a casualty insurance company show that, in the past, its clients have had a mean of  1.8  auto accidents per day with a variance of  0.0036 . The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to  0.0036 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis  H0  and the alternative hypothesis  H1  that we would use for this test. H0:H1:

Suppose that we would like to test the following hypotheses on the population correlation coefficient ρ: H0: ρ ≤ 0 and H1: ρ > 0. The sample correlation coefficient (r) for a sample with 7 observations (n = 7) on x and y is 0.35 . Then the test statistic t has a value of

An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG Corporation are approximately normally distributed with a mean of 660 days and a variance of 15,625. BIG Corporation claims that the variance of its electric bulbs is less than 15,625. Suppose that we want to carry out a hypothesis test to see if BIG Corporation's claim is correct. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. H0:   H1:

The record of a casualty insurance company show that , in the past, its clients have had a mean of 1.7 auto accidents per day with a variance of 0.0025. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. Stat the null hypothesis H0 and the alternative hypothesis H1 that we would use this test. H0:  ____ H1: _____