Question

Suppose that you know that the weight of standard poodles is Normally distributed with a standard deviation of 4 pounds. You take an SRS of 10 poodles and find their average weight to be 52 pounds.  

Perform a significance test with this data to see if the average weight of standard poodles is 49 pounds or if it is actually larger than that. Use a 3% significance level. Fill in the blanks with each requested value. Write all numbers as decimals, rounding to 3 places after the decimal.

Test Statistic =

p-value =

Answer 1

Here we have given that,

n= Number of poodles = 10

= sample mean weight =52 pounds

= Population standard deviation=4 pounds

The below mentioned necessary assumption is satisfied for this hypothesis test (one sample z-test).

• The data are simple random sample values form the population.
• The weight of standard poodles is normally distributed.
• The Population standard deviation is known we are using the one sample z-test to test the hypothesis.

Claim: To check whether the population mean weight of standard poodles is larger than 49 pounds.

The null and alternative hypothesis is as follows

pounds

Versus

pounds

where, = the population mean weight of standard poodles

This is the Right one-tailed test.

Now, we can find the test statistic

z-statistics =

                  =

                  = 2.37

The Test statistic is 2.37

Now we can find the P-value

This is two tailed test

Now, we can find the P-value

P-value =P(Z > z-statistics) as this is the right one tailed test

=1 - P( Z < 2.37)

                =1- 0.99111 Using standard normal z table see the value corresponding to the z=2.37

= 0.009

we get the P-value is 0.009

Decision:

= level of significance=0.03

P-value (0.009) less than (<) 0.03 ()

Conclusion:

we reject Ho (Null Hypothesis)

There is sufficient evidence to conclude that the population mean weight of standard poodles is larger than 49 pounds.