Math  /  Data & Statistics

QuestionUse a t-test to test the claim about the population mean μ\mu at the given level of significance α\alpha using the given sample statistics. Assume the population is normally distributed. Claim: μ8300;α=0.10\mu \geq 8300 ; \alpha=0.10 Sample statistics: xˉ=8100,s=460,n=25\bar{x}=8100, s=460, n=25
What are the null and alternative hypotheses? A. H0:μ8300\mathrm{H}_{0}: \mu \neq 8300 B. H0:μ=8300H_{0}: \mu=8300 Ha:μ=8300H_{a}: \mu=8300 Ha:μ8300H_{a}: \mu \neq 8300 C. H0:μ8300H_{0}: \mu \geq 8300 D. H0:μ8300H_{0}: \mu \leq 8300 Ha:μ<8300H_{a}: \mu<8300 Ha:μ>8300H_{a}: \mu>8300
What is the value of the standardized test statistic? The standardized test statistic is \square (Round to two decimal places as needed.)

Studdy Solution
Calculate the standardized test statistic using the formula for the t-statistic:
t=xˉμs/nt = \frac{\bar{x} - \mu}{s/\sqrt{n}}
Substitute the given values:
t=81008300460/25t = \frac{8100 - 8300}{460/\sqrt{25}}
Calculate the denominator:
46025=4605=92\frac{460}{\sqrt{25}} = \frac{460}{5} = 92
Calculate the t-statistic:
t=8100830092=200922.17t = \frac{8100 - 8300}{92} = \frac{-200}{92} \approx -2.17
The standardized test statistic is:
2.17\boxed{-2.17}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord