It was reported that 5% of adults over the age of 55 have a problem with gamblin
ID: 3157076 • Letter: I
Question
It was reported that 5% of adults over the age of 55 have a problem with gambling, but one researcher believes the proportion is actually higher in her state. She wants to test the hypotheses H_0: p = 0.05 versus the alternative H_A: p > 0.05. If in a random sample of n=942 people over the age of 55, she found that 60 had a problem with gambling. Compute the p-value for this test and use it to make a conclusion at the 1% level of significance. Calculated Test Statistic: p-value: Decision: Conclusion: Compute the probability of type II error if the true proportion of adults with a gambling problem is actually 7%.Explanation / Answer
1.
a)
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.05
Ha: p > 0.05
As we see, the hypothesized po = 0.05
Getting the point estimate of p, p^,
p^ = x / n = 0.063694268
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.00710103
Getting the z statistic,
z = (p^ - po)/sp = 1.928490279 [ANSWER, TEST STATISTIC]
*************************************************
As this is a 1 tailed test, then, getting the p value,
p = 0.026897086 [ANSWER, P VALUE]
************************************************
As P > 0.01, we FAIL TO REJECT THE NULL HYPOTHESIS. [DECISION]
*********************************************
Hence, there is no significant evidence at 0.01 level that more than 5% of adults over the age of 55 have a problem with gambling. [CONCLUSION]
*******************************************
Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.