Question

Q1) Last year the government made a claim that the average income of the American people was $33,950. However, a sample of 28 people taken recently showed an average income of $34,076 with a standard deviation of $324. Is the government’s estimate too low? Conduct a significance test to see if the true mean is more than the reported average. Use α=0.05.

(a) State the null and alternative hypothesis.

(b) Calculate the test statistic.

(c) Calculate the p-value. Round to 4 decimal places

(d) Make a decision at the 0. 05 significance level to reject Ho or fail to reject Ho.

(e) Write your conclusion in the context of the claim.

Q2) A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer’s disease will experience nausea. In a random sample of 250 patients, 23 experienced nausea. Perform a significance test at the 5% significance level to test this claim.

(a) State the null and alternative hypothesis.

(b) Calculate the test statistic.

(c) Calculate the p-value. Round to 4 decimal places

(d) Make a decision at the 0. 05 significance level to reject Ho or fail to reject Ho.

(e) Write your conclusion in the context of the claim.

Answer 1

Q1

A)

The null and Alternative hypothesis is as follows:

Null Hypothesis: the average income of the American people was not greater than 33950.

Anlternative : the average income of the American people was greater then 33950.

b)

Calculate the test statistic.

c)

Calculate p- value

d) The level of significance is

Compare p- value with the level of significance

Here, the p- value is less than the significance so reject the null hypothesis.

e)

Hence, conclude that there is sufficient evidence to conclude that the average income of the American people was greater than 33950.