12 .Find the p-value for the following hypothesis test. H0: 20, H1: <20, n=80, x=18.75, =4.5

a.0.0066

b.-2.48

c.0.4934

d.0.0033

15.Given the following hypotheses: H0 = 500, H1 500.For a random sample of 15 observations, the sample mean was 507 and the sample standard deviation 6. Using the 0.05 significance level state the decision rule.

a.Reject H0 and accept H1 if the test statistic is between 2.145 and +2.145

b.Do not reject H0 if the test statistic falls between 2.145 and +2.145

c.Reject H0 and accept H1 if the test statistic is between 2.132 and +2.132

d.Do not reject H0 if the test statistic falls between 2.132 and +2.132

17.Find the p-value for the following hypothesis test.

z=x/n=46.8448.3/55=2.50.z=x-/n=46.8-448.3/55=-2.50.

a.0.4938

b.0.0062

c.0.0031

d.0.0124

19 .Of 150 teens who tried a new texting cell phone, 110 rated it as easy to use. Of 180 adults who tried the same phone only 98 found it easy to use. Is there a significant difference in the proportion of adults and teens who rated the new phone as easy to use? The null and alternate hypotheses are:

H₀:p₁p₂ 0

H₁:p₁p₂< 0

a.True

b. False

23.If in a two-tailed, two-sample test of proportions for independent samples, we fail to reject the null hypotheses, then we can conclude that

a.a difference exists between the population proportions.

b.we have no evidence that a difference exists between the population proportions.

c.the difference between sample proportions is definitely zero.

d.the difference between the population proportions is 1.

24.A sample of 200 observations from population 1 indicated that x1 is 160. A sample of 220 observations from population 2 indicated that x2 is 165. Compute the pooled proportion.

a.0.012

b.1.55

c.0.77

d.0.65

Please show calculations.