H0: = 15 Ha: 15 A sample of 40 provided a sample mean of 14.12. The population s

Question

H0: = 15

Ha: 15

A sample of 40 provided a sample mean of 14.12. The population standard deviation is 3.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 4 decimals)?

c. Using = .05, can it be concluded that the population mean is not equal to 15?

Answer the next three questions using the critical value approach.

d. Using = .05, what are the critical values for the test statistic? (+ or -)

e. State the rejection rule: Reject H0 if z is
Select
greater than or equal to
greater than
less than or equal to
less than
equal to
not equal to
Item 5
the lower critical value and is
Select
greater than or equal to
greater than
less than or equal to
less than
equal to
not equal to
Item 6
the upper critical value.

f. Can it be concluded that the population mean is not equal to 15?

Explanation / Answer

Set Up Hypothesis
Null Hypothesis H0: U=15
Alternate Hypothesis H1: U!=15
Test Statistic
Population Mean(U)=15
Given That X(Mean)=14.12
Standard Deviation(S.D)=3
Number (n)=40
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=14.12-15/(3/Sqrt(40)
Zo =-1.8552
| Zo | =1.8552
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =1.8552 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != -1.8552 ) = 0.0636
Hence Value of P0.05 < 0.0636, Here We Do not Reject Ho

[ANSWERS]
1.Zo =-1.86
2. P= 0.0636
3. No, we don't hv evidence to suport not equal 15
4. +1.96,-1.96

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