For this lesson, we are going to take our problem scenarios from last lesson and create hypothesis tests instead of confidence intervals. Just like confidence intervals, hypothesis tests make inferences about population values (*p* or μ)

1) During an election, an exit poll is taken on 400 randomly selected voters and 214 of those polled voted for Candidate “Jim”. A majority is needed to win the election. We want to see if we can conclude that the majority will vote for Candidate “Jim” based on our sample proportion from the exit poll. The alternative hypothesis (Ha) is what we are testing to see and the null hypothesis (Ho) is the value that we are testing “against”. (See page 402–the null hypothesis is a statement that the parameter takes a particular value, while the alternative hypothesis is that the parameter falls in some alternative range of values). We test to see if we can reject the null hypothesis and conclude the alternative hypothesis.

A)

i) State the null and alternative hypotheses using proper Statistical Notation (*p*for population proportion).

ii) Is this a one-sided alternative hypothesis (> or <) or a two-sided alternative hypothesis (≠)?

iii) What is the SEo. Show all work.

iv) Calculate your test statistic (we use a Z test statistic with proportions). Show all work.

v) Go to the Z Table in the back of the text and determine the p-value for our Z test statistic value. If we have a > alternative, we want the right-tail p-value. If we have a < alternative, we want the left-tail (cumulative probability) p-value. If we have a ≠ alternative, we want the two-tailed p-value.

vi) What is our conclusion based on the p-value? (Can we declare Candidate “Jim” the winner?) Why?

B) Now, assume 900 voters were polled and 482 indicated that they voted for Candidate “Jim”.

i) What is the SEo. Show all work. Is the SEo the same, larger or smaller than in part A?

ii) Calculate your test statistic (we use a Z test statistic with proportions). Show all work Is the Z value the same, larger or smaller than in part A? Why?.

iii) Go to the Z Table in the back of the text and determine the p-value for our Z test statistic value. If we have a > alternative, we want the right-tail p-value. If we have a < alternative, we want the left-tail (cumulative probability) p-value. If we have a ≠ alternative, we want the two-tailed p-value

iv) What is our conclusion based on the p-value? (Can we declare Candidate “Jim” the winner?) Why?

2) In past years,the population mean score on an achievement test given nationwide was 235. You believe that the population mean now differs from 235. To test this, you randomly sampled 25 students. The sample mean was 240 and the sample SD was 15.

A)

i) State the null and alternative hypotheses using proper Statistical Notation (μfor population mean).

ii) Is this a one-sided alternative hypothesis (> or <) or a two-sided alternative hypothesis (≠)?

iii) What is the SE. Show all work.

iv) Calculate your test statistic (we use a *t* test statistic with means). Show all work.

v) Go to the *t* Table in the back of the text and determine the p-value for our *t*test statistic value. If we have a > alternative, we want the right-tail p-value. If we have a < alternative, we want the left-tail (cumulative probability) p-value. If we have a ≠ alternative, we want the two-tailed p-value. (you have to determine the DF row to use and provide the “range” that the p-value is in since you cannot provide a specific p-value given the table).

vi) What is our conclusion based on the p-value?

B)Now assume our sample size is 81, with a sample mean of 240 and a sample SD of 15.

i) Calculate the SE. Show all work.

ii) Calculate your test statistic (we use a *t* test statistic with means). Show all work.

iii) Is the *t* test statistic the same, larger or smaller than in part A above?

Why?

iv) Go to the *t* Table in the back of the text and determine the p-value for our*t* test statistic value. If we have a > alternative, we want the right-tail p-value. If we have a < alternative, we want the left-tail (cumulative probability) p-value. If we have a ≠ alternative, we want the two-tailed p-value.

v) What is our conclusion based on the p-value?