Question

2) A study done in 2016 showed that 38% of drivers admitted to text messaging while driving. A researcher decides to conduct another study to see if things have changed since then. The researcher wants the new study to have no more than a confidence level of 95%. results? 4% error with a How many responses does the researcher need to achieve these b) There is not enough evidence to reject the claim d) There is not enough evidence to support the claim a) There is enough evidence to reject the claim c) There is enough evidence to support the claim 5) A local citizen's group is upset with land development in Brick. They claim that the amount of sprawl has increased more than 65% over the last four years. Ifyou were on a politician's staff and were told to test the group's claim, which of the three types of hypothesis tests (left-tail, right-tail, or two-tail) would indicate that the claim is incorrect? You must explain your answer to get credit. 6) A high school claims that at least 65% of their students plan on going to college. A random survey of 144 students resulted in 75 of the students saying they plan on going to college. At .05 test the claim. Show all necessary steps. Interpret your answer in a sentence or two. 7) You test 19 samples of water and find that the mean concentration of chlorine in the water is 150 mg/l with a standard deviation of 3 1 mg/l. Construct a 95% confidence interval for your results and draw the interval. 6) The USDA has established limits for salmonella in chicken to be sold for human consumption. An inspector reports that the level has been exceeded at a particular company that is the major source of jobs in a small town. A hypothesis test by the USDA is performed to investigate the report. There are two kinds of errors that can result: Ho can be rejected when it should not be. and Ho can fail to be rejected when it should have been. Describe the possible consequences of each error. Which do you think is more serious? 24

Answer 1

I would solve 6th question

We would use the hypothesis test for proportion

Here value of proportion p=0.65

Let us first find the value of np=0.65(144)=93.6 and nq=144(0.35)=50.4 which are both greater than 5

So We would use Z test

The claim is that at least 65% of students plan to  going to college

Null hypothesis:Ho:p=0.61

Alternate hypothesis:p>0.61

Because it is one tailed t test

and level o f significance =0.05

So critical value will be 1.645

Here sample proportion will be given as

75 n 144 p =-=-= 0.52

So standardized test statstic is

0.52 0.65 Z =-pl/n-V0.52(0.48)/144

absolute value of Z stat is greater than Z critical

Z stat>Z critical

we would reject null hypothesis

so our claim is true that at least 65% of students are planning to going to college