Respuesta :
Answer:
(a) The value [tex]\bar x[/tex] = 72.3 is 1.21 standard deviations below the null value of μ.
(b) The mean drying time of paint is not less than 74.
Step-by-step explanation:
The hypothesis for the single mean test is:
H₀: μ = 74 vs. Hₐ: μ < 74.
The information provided is:
σ = 7
n = 25
As the population standard deviation is known, we will use a z-test for single mean.
(a)
The z-score is a Normal distribution with mean 0 and variance 1. It is also defined as the number of standard deviations a raw score is from the mean.
The z-score for sample mean is given by:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
If [tex]\bar x[/tex] = 72.3 compute the corresponding z-score as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{72.3-74}{7/\sqrt{25}}\\=-1.21[/tex]
Thus, the value [tex]\bar x[/tex] = 72.3 is 1.21 standard deviations below the null value of μ.
(b)
So the test statistic is, z = -1.21.
Compute the p-value of the test as follows:
[tex]p-value=P(Z<z)\\=P(Z<-1.21)\\=0.1131[/tex]
*Use a z-table.
The decision rule says to, reject the null hypothesis if the p-value is less than the significance level α = 0.01 and vice-versa.
p-value = 0.1131 < α = 0.01
The null hypothesis was failed to be rejected.
Thus, the mean drying time of paint is not less than 74.
