Section 7.2: Hypothesis Testing for the Mean(Large Samples) 1. Use the method sp

Question

Section 7.2: Hypothesis Testing for the Mean(Large Samples)

1.     Use the method specified to performthe hypothesis test for the population

mean . WeatherBug say that the mean daily high forDecember in a large Florida city is 76o  F. WFLA weathersuspects that this temperature is not accurate. A hypothesis testis performed the determine if the mean is actually lower than76o  F. Assume that the population standarddeviation of = 5.6o F. A sample of mean dailytemperatures for December over the past 40 years gives x(with barover top of x)=74o F. At = 0.01, does the data providesufficient evidence to conclude that the mean temperature is lowerthan 76o F.

a. Use the critical value z0method from the normal distribution.

1.    H0:

Ha :

2.    a=

3.    Teststatistics:

4.    P-value orcritical z0 or t0.   

5.    RejectionRegion:

6.   Decision:

7.    Interpretation:

b.    Use the P-valuemethod.

1.    H0:

Ha :

2.    a=

3.    Teststatistics:

4.    P-value orcritical z0 or t0.

5.    RejectionRegion:

6.   Decision:

7.   Interpretation:

Explanation / Answer

Let be the mean daily high temperature forDecember in a large Florida city.
1. H0 : = 76
    Ha : < 76

2. = 0.01

3.Test statistic:

Since the population standard deviation is known, thetest statistic for testing H0 is

z = (x- 76)/ (/Sqrt(n))follows a Standard normal distribution

Here it is given that xbar = 74, = 5.6 and n=40.

Thus, the test statistic,

z = (x- 76)/ (/Sqrt(n))

   =(74-76)/(5.6/Sqrt(40))

   = -2/0.8854

   = - 2.2588

4.P-value or critical z0 or t0.

Since = 0.01, the critical value z0 is given by

Critical z0 = -2.33
5.Rejection Region:

Reject H0 if z < -2.33
6.Decision:

Since z = -2.2588 > -2.33, we donot reject the null hypothesis H0.
7.Interpretation:
   The data do not provide sufficient evidence toconclude that the mean temperature is lower than 76 F at 1% levelof significance.

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