76 73 69 70 Based on these data, I would reject H 0 at level: The time (in numbe

Question

76

73

69

70

Based on these data, I would reject H0 at level:

The time (in number of days) until maturity of a certain variety of hot pepper is Normally distributed, with mean and standard deviation = 2.4. This variety is advertised as taking 70 days to mature. I wish to test the hypotheses H0: = 70, Ha: > 70, so I select a simple random sample of four plants of this variety and measure the time until maturity. The four times, in days, are

76

73

69

70

Based on these data, I would reject H0 at level:

None of the above 0.05 but not at level 0.01. 0.10 but not at level 0.05. 0.01.

Explanation / Answer

Set Up Hypothesis
Null Hypothesis H0: U=70
Alternate Hypothesis H1: U>70
Test Statistic
Population Mean(U)=70
Given That X(Mean)=72
Standard Deviation(S.D)=2.4
Number (n)=4
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=72-70/(2.4/Sqrt(4)
Zo =1.6667
| Zo | =1.6667
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =1.6667 & | Z | =2.33
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
AT 0.01 LOS
P-Value : Right Tail - Ha : ( P > 1.6667 ) = 0.0478
Hence Value of P0.01 < 0.0478, Here We Do not Reject Ho

AT 0.05 LOS
P-Value : Right Tail - Ha : ( P > 1.6667 ) = 0.0478
Hence Value of P0.05 > 0.0478, Here we Reject Ho

[ANSWER]
0.05 but not at level 0.01

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