Respuesta :
Answer:
The p-values are:
(a) p-value = 0.023 (e) p-value = 0.001
(b) p-value = 0.008 (f) p-value = 0
(c) p-value = 0.1096 (g) p-value = 0.005
(d) p-value = 0.3446
Step-by-step explanation:
The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or greater than what was truly observed.
(a)
The alternate hypothesis is:
Hₐ: μ > μ₀
The test statistic value is, Z = 2.0.
Compute the p-value as follows:
[tex]p-value=P(Z>2.0)\\=1-P(Z<2.0)\\=1-0.9773\\=0.0227\\\approx0.023[/tex]
*Use a z-table.
The p-value of 0.023 implies that the probability of getting the mean value greater than or equal to μ₀ is 0.023.
(b)
The alternate hypothesis is:
Hₐ: μ < μ₀
The test statistic value is, Z = -2.4.
Compute the p-value as follows:
[tex]p-value=P(Z<-2.4)\\=1-P(Z<2.4)\\=1-0.9918\\=0.0082\\\approx0.008[/tex]
*Use a z-table.
The p-value of 0.008 implies that the probability of getting the mean value as extreme as μ₀ is 0.008.
(c)
The alternate hypothesis is:
Hₐ: μ ≠ μ₀
The test statistic value is, Z = -1.6.
Compute the p-value as follows:
[tex]p-value=2P(Z>-1.6)\\=2[1-P(Z<1.6)]\\=2[1-0.9452]\\=0.1096[/tex]
*Use a z-table.
The p-value of 0.1096 implies that the probability of getting the mean value as extreme as μ₀ is 0.1096.
(d)
The alternate hypothesis is:
Hₐ: μ < μ₀
The test statistic value is, Z = -0.4.
Compute the p-value as follows:
[tex]p-value=P(Z<-0.4)\\=1-P(Z<0.4)\\=1-0.65542\\=0.34458\\\approx0.3446[/tex]
*Use a z-table.
The p-value of 0.3446 implies that the probability of getting the mean value as extreme as μ₀ is 0.3446.
(e)
The alternate hypothesis is:
Hₐ: μ < μ₀
The test statistic value is, Z = -3.16.
Compute the p-value as follows:
[tex]p-value=P(Z<-3.16)\\=1-P(Z<3.16)\\=1-0.99921\\=0.00079\\\approx0.001[/tex]
*Use a z-table.
The p-value of 0.001 implies that the probability of getting the mean value as extreme as μ₀ is 0.001.
(f)
The alternate hypothesis is:
Hₐ: μ > μ₀
The test statistic value is, Z = 5.0.
Compute the p-value as follows:
[tex]p-value=P(Z>5.0)\\=1-P(Z<5.0)\\=1-(\approx1)\\=0[/tex]
*Use a z-table.
The p-value of 0 implies that the probability of getting the mean value as extreme as μ₀ is 0.
(g)
The alternate hypothesis is:
Hₐ: μ ≠ μ₀
The test statistic value is, Z = 2.8.
Compute the p-value as follows:
[tex]p-value=2P(Z>2.8)\\=2[1-P(Z<2.8)]\\=2[1-0.99744]\\=0.00512\\\approx0.005[/tex]
*Use a z-table.
The p-value of 0.005 implies that the probability of getting the mean value as extreme as μ₀ is 0.005.
