Question

# Q1) Last year the government made a claim that the average income of the American people...

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.

Solution: (a) Null hypothesis Alternative hypothesis (b) the test statistic (c) P value is 0.0247 TDIST(2.058,27,1)P value by using Excel command. (d) at the 0. 05 significance level to reject Ho Since, p value = 0.0247 < 0.05 (e) We have sufficient evidence to say that , at 0.05 level of significance that, the true mean is more than the reported average. Q2) (a) Null hypothesis Alternative hypothesis (c) P value is 0.3365 NORMSDIST(-0.422) P value by using Excel command. (d) at the 0. 05 significance level fail to reject Ho. Since

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