Trials in an experiment with a polygraph include 96 results that include 22 cases of wrong results and 74 cases of correct results. use a 0.01 significance level to test the claim that such polygraph results are correct less than 80% of the time based on the results should polygraph test results be prohibited as evidence in trials? identify the null hypothesis, alternative hypothesis, test statistics, p value, conclusion about null hypotheses and final conclusion that address the original claim. use the p value methos. use the normal distribution as an approximation of the binomial distribution. a. i dentify the null and alternative hypothesis b. the test staistic is z= (round to two decimals) c. the p value is=( rounds to four decimals) d. identify the conclusion about the null hypotheses and the final conclusion that address the original claim. choose (fail to reject, reject) h0. there choose(is, is not) sufficient evidence to support the claim that the polygraph result are correct less than 80% of time. answer h0: p ≥ 0.80 ha: p < 0.80 estimated p = 74 / 98 = 0.7551 variance of proportion = p*(1-p)/n = 0.8(0.2)/98 =0.0016327 s. d. of p is sqrt[0.001633] = 0.0404 z = ( 0.7551 - 0.8 ) / 0.0404 = -1.1112 p-value = p( z < -1.1112) = 0.1335 since the p-value is greater than 0.05, we do not reject the null hypothesis. based on the results there is no evidence that polygraph test results should be prohibited as evidence in trials.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.