In this problem, assume that the distribution of differences is approximately normal.
Note: For degrees of freedom
d.f. not in the Student's
t
table, use the closest
d.f. that is
smaller. In some situations, this choice of
d.f. may increase the
P-value by a small amount and therefore produce a slightly more "conservative" answer.
A survey of houses and traditional hogans was made in a number of different regions of the modern Navajo Indian Reservation. The following table is the result of a random sample of eight regions on the Navajo Reservation.
Extracted text: Sketch the sampling distribution and show the area corresponding to the P-value. b a P-value P-value -t -t d P-value P-value -t ot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. O Reject the null hypothesis, there is sufficient evidence to claim that the mean number of inhabited houses is greater than that of hogans. O Reject the null hypothesis, there is insufficient evidence to claim that the mean number of inhabited houses is greater than that of hogans. O Fail to reject the null hypothesis, there is insufficient evidence to claim that the mean number of inhabited houses is greater than that of hogans. O Fail to reject the null hypothesis, there is sufficient evidence to claim that the mean number of inhabited houses is greater than that of hogans.
0; H,: Hd = 0; right-tailed O Ho: Hd = 0; H: Hg < 0;="" left-tailed="" o="" ho:="" hd="0;" h:="" hd=""> 0; right-tailed O Ho: Hd = 0; H,: Hg + 0; two-tailed (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately normal distribution. O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. O p-value > 0.250 O 0.125 < pp-value="">< 0.250="" o="" 0.050="">< p-value="">< 0.125="" o="" 0.025="">< p-value=""><0.050 o="" 0.005="">< p-value="">< 0.025="" o="" p-value="">< 0.005="" "/="">
Extracted text: In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student'st table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. A survey of houses and traditional hogans was made in a number of different regions of the modern Navajo Indian Reservation. The following table is the result of a random sample of eight regions on the Navajo Reservation. Area on Navajo Reservation Bitter Springs Rainbow Lodge Number of Inhabited Houses Number of Inhabited Hogans 16 11 18 14 Kayenta Red Mesa 68 46 32 Black Mesa 11 15 Canyon de Chelly Cedar Point Burnt Water 28 47 50 17 50 18 Does this information indicate that the population mean number of inhabited houses is greater than that of hogans on the Navajo Reservation? Use a 5% level of significance. (Let d = houses - hogans.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: Hd > 0; H,: Hd = 0; right-tailed O Ho: Hd = 0; H: Hg < 0;="" left-tailed="" o="" ho:="" hd="0;" h:="" hd=""> 0; right-tailed O Ho: Hd = 0; H,: Hg + 0; two-tailed (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately normal distribution. O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. O p-value > 0.250 O 0.125 < pp-value="">< 0.250="" o="" 0.050="">< p-value="">< 0.125="" o="" 0.025="">< p-value=""><0.050 o="" 0.005="">< p-value="">< 0.025="" o="" p-value="">< 0.005>