Answer to Question #350644 in Statistics and Probability for Matt

Question #350644

A certain group of welfare recipients receives relief goods with a mean amount of Php 500.00 per week. A random sample of 75 recipients is survived and found that the mean amount of relief goods they received in a week is Php 600 and a standard decision of Php. 50.00. Test the claim at 1% level of significance is not Php 500.00 per week and assume that the population is approximately normally distributed. Which of the following is correct null and alternative hypothesis, in symbol?


1
Expert's answer
2022-06-15T13:04:38-0400

The following null and alternative hypotheses need to be tested:

H0:μ=500H_0:\mu=500

H1:μ500H_1:\mu\not=500

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

Based on the information provided, the significance level is α=0.01,\alpha = 0.01, df=n1=74df=n-1=74 and the critical value for a two-tailed test is tc=2.643913.t_c =2.643913.

The rejection region for this two-tailed test is R={t:t>2.643913}.R = \{t:|t|>2.643913\}.

The t-statistic is computed as follows:



t=xˉμs/n=60050050/75=17.3205t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}=\dfrac{600-500}{50/\sqrt{75}}=17.3205


Since it is observed that t=17.3205>2.643913=tc,|t|=17.3205>2.643913=t_c, it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value for two-tailed, df=74df=74 degrees of freedom, t=17.3205t=17.3205 is p=0,p=0, and since p=0<0.01=α,p=0<0.01=\alpha, it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean μ\mu is different than 500.00, at the α=0.01\alpha = 0.01 significance level.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment