What type of error have commited if null hypothesis is false

Reference no: EM13132177

Suppose you randomly choose a sample of 25 observations from a normal distribution. You then use those observations to estimate the mean of the population.

a. Assuming that we would consider anything from 159 to 161 as "equal to 160," and that we know that the standard deviation of the population is 1.0, estimate the probability that we will be able to determine that the mean is different than 160 if it actually is different than 160. Use α = 0.05. (Hint: this is equivalent to saying, "what is the probability that we will reject the null hypothesis given that it is false?")
b. If the mean of the observations is 158.7, what would you guess the mean of the population is (on the basis of the sample)? (I do not want the confidence interval - just report your estimate of the population mean.)
c. Suppose the population is N(160.0, 1.2). It is possible that you could extract a sample from that population such that a hypothesis test on that sample would reject the null hypothesis, even though it is true. If we use α = 0.01, what are the chances of this happening? (Hint: this is equivalent to saying, "what is the probability that we would reject the null hypothesis given that it is true?")
d. If you were to accept the null hypothesis, even though the null hypothesis was false, what type of error would you have commited?

Reference no: EM13132177

Questions Cloud

Calculate controlling interest in consolidated net income : Now assume that the merchandise mentioned was included in Pearce's inventory, having been purchased from Searl. Calculate controlling interest in consolidated net income for 2011 and 2012.

Finite field proof : Let F be a finite field. Prove that F[x] contains infinitely many primes. (note that over an infinite field the polynomials of degree 1 are an infinite set of primes in the ring of polynomials).

Governmental units that issue tax- supported debt : Which of the following is a true statement about governmental units that issue tax- supported debt to finance capital projects?

Determining number code puzzle : An AE student named Seoung devises a coded system of arithmetic for keeping his financial information private. His coded system of arithmetic is identical to the usual one except that each digit 0 to 9 has a value different than from standard arit..

What type of error have commited if null hypothesis is false : If you were to accept the null hypothesis, even though the null hypothesis was false, what type of error would you have commited?

Calculate the specific enthalpy of o2 in this state : Oxygen at 150 K and 41.64 atm has a tabulated specific volume of 4.684 cm3/g and a specific internal energy of 1706 J/mol.

Explain palladium catalyst forming compound b : Unknown compound A (C8H12) is reacted with H2 (excess) in the presence of a palladium catalyst forming compound B (C8H16). In addition when compound A is reacted with O3 followed by zinc and acetic acid the following two compounds are formed

What should company report as its deferred income tax : What should company report as its deferred income tax liability as of the end of its first year of operations.

What is the mass percentage of salt in the mixture : Table salt and sugar are accidentally mixed A 4.90 g sample is burned and 2.20-g of CO2 is produced What is the mass percentage of salt in the mixture?

User Account

All Pages