Question

A sample of n sludge specimens is selected and the p ollowing situations? of each one is determined. The one sample t test wil then be used to see if there is compelling evidence for concluding that true average ph is less than 7.0. What conclusion is appropriate in each of the O Reject the null hypothesis. Thareis sutficient evidence that the true average pH is less than 7.0 Reject the nul hypothesis. There is not sufficient evidence that the true average pH ts less than 7.0. 。Do not reject the null hypothesis. There is sufficient evidence that the true average pH less than 7.0. O Du not reject the null hypothesis. There is ot sufficient evideice that the true average pH is less than 7.0 (b) n-12, t-_3.8, α-0.01 O Reject tha null hypathesis. Thare is sufficiant evidanca that the trua avarage pH is lass than 7.D O Reject the nul hypothasis. Thare is not sufficient avidence that the true averaga pH is less than 7.0 Do not reject tne null hypothesis. There is sufficient evidence that the true average pH ts less than 7.0. O Do not reject the null hypothesis, There is not sufficient evidence that the true average plH is less than 7.0. ()n-11, t-1.5,a-0.05 O Reject the null hypothesis. There is sufhicient evidence that the true average pH is less than 7.0 O Reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0 O Du not reject the null hypothesis. There is sufficient evidence that the true average pH is less thai 7.0. O Do not reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0 (d) n-6, t-0.5, α-0.05 O Reject the nul hypothasis. Thareis sutficiant evidence that the true avarage pH is less than 7.0 Reject the n녜 hypothesis. There is not sufficient evidence that the true average pH ts less than 7,0. 。Do not reject the null hypothesis. There is sufficient evidence that the true average pH e less than 7.0. O Do not reject the null hypothesis. There is not sufficient evidernce that the true average pH is less than 7.0. O wa wouid fail to rajact the nul hypothasis for any significanca leval at or halow.997, O We wouid fail to reject the nul hypothesis for any signiicance level at or above 0.997 O We would reject the null hypothesis tor any significance level at or above 0.003 O We would reject the null hypothesis for any significance level at or below 0.003.

Answer 1

The table is given as:

n	t-calc	Level of significance	t-critical	Accept/Reject
9	-2.2	0.05	-1.85954803	Reject
12	-3.8	0.01	-2.71807918	Reject
11	-1.5	0.05	-1.8124611	Accept
6	0.5	0.05	-2.01504837	Accept

(a)

Reject the null hypothesis. There is sufficient evidence that the true pH is less than 7.0

(b)

Reject the null hypothesis. There is sufficient evidence that the true pH is less than 7.0

(c)

Do not reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0

(d)

Do not reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0

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