Question

It is assumed that the mean weight of a Labrador retriever is 70 pounds. A breeder claims that the average weight of an adult male Labrador retriever is not equal to 70 pounds. A random sample of 45 male Labradors weigh an average of 72.5 pounds with a standard deviation of 16.1 pounds. Test the breeder's claim at

Answer 1

Complete Question:

It is assumed that the mean weight of a Labrador retriever is 70 pounds. A breeder claims that the average weight of an adult male Labrador retriever is not equal to 70 pounds. A random sample of 45 male Labradors weigh an average of 72.5 pounds with a standard deviation of 16.1 pounds. Test the breeder's claim at \alpha=0.04

a)State null and alt hypothesis

b)determine t statistics

c)compute the P value

d) decision about the test

Answer:

a)Null Hypothesis
`H_0:\mu=70`

Alternative Hypothesis
`H_1=\mu \\eq70`

b)
`t=1.042`

c)
`TDIST(1.042)=0.30310338`

d)We reject the alternative hypothesis

Explanation:

From the question we are told that:

Population mean
`\mu=70`

Sample size
`n=45`

Sample mean
`\=x=72.5`

Standard deviation
`\sigma=16.1 pounds.`

Significance level
`\alpha=0.04`

a

Generally the Hypothesis is mathematically given by

Null Hypothesis
`H_0:\mu=70`

Alternative Hypothesis
`H_1=\mu \\eq70`

b) Generally the Equation for test statistics is mathematically given by

`t=(\=x-\mu)/((s)/(√(n) ) )`

`t=(72.5-70)/((16.1)/(√(45)))`

`t=1.042`

c)

Generally From T distribution table P value is mathematically given by

`TDIST(1.042)=0.30310338`

d)

Therefore as p value is greater tab significance level

`0.30310338>0.04`

The Test statistics does nt fall in the rejection rejoin

Therefore

We reject the alternative hypothesis

Answer 2

z(s) is in the acceptance region we accept H₀. We don´t have enough evidence to support the breeder´s claim

Explanation:

We will test the breeder´s claim at 95% ( CI) or significance level

α = 5 % α = 0,05 α /2 = 0,025

Sample Information:

sample size n = 45

sample mean x = 72,5 pounds

Sample standard deviation s = 16,1

1.-Hypothesis Test:

Null Hypothesis H₀ x = 70

Alternative Hypothesis Hₐ x ≠ 70

Alternative hypothesis contains the information about what kind of test has to be developed ( in this case it will be a two-tail tets)

2.-z (c) is from z-table z(c) = 1,96

3.- z(s) = ( x - 70 ) / 16,1 / √45

z(s) = (72,5 -70 ) *√45 / 16,1

z(s) = 2,5 * 6,71 / 16,1

z(s) = 1,04

4.-Comparing z(s) and z(c)

z(s) < z(c)

Then z(s) is in the acceptance region we accept H₀. We don´t have enough evidence to support the breeder´s claim