Question

A drug company is considering marketing a new local anesthetic. The effective time of the the drug company is currently producing has a normal distribution average anesthetic of 12 minutes. The chemistry of the esthetic with an of 7.4 minutes with a standard deviation but the mean new is such that the effective time shoul be with the same standard deviation, effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of 36 in a sample mean of 7.1. A hypothesis test will be done to size results help make the decision. The appropriate hypotheses are:_______
1. For a test with a level of significanoe of 0.10, the critical value would be__________.
2. The value of the test statistic is:___________.

Answer 1

Answer:

Step-by-step explanation:

The question has some errors. The correct question is:

A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with an average of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normal with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1. done to help make the decision.

The solution would be :

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 7.4

For the alternative hypothesis,

µ < 7.4

1, Since α = 0.1, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.1/2 = 0.05

The z score for an area to the left of 0.05 is - 1.645

For the right, α/2 = 1 - 0.05 = 0.95

The z score for an area to the right of 0.95 is 1.645

Therefore, the critical values are z = - 1.645 and z = 1.645

2) Since the population standard deviation is given, the test statistic, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 7.4

x = 7.1

σ = 1.2

n = 36

z = (7.1 - 7.4)/(1.2/√36) = - 1.5