Mathematics: Use a t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed. Claim: μ ≥8 300, α = 0.10 Sample statistics: x = 8000, s = 440, n = 24 A. What are the null and alternative hypotheses? B. What is the value of the standardized test statistic? C. What is the p-value? D. Decide whether to reject or fail to reject the null hypothesis.

choice 1) An hour is 3600 times as long as a secondStep-by-step explanation:60 x 60 = 3600...

Use a t-test to test the claim about the population

wow65

31.01.2022

The null hypothesis is $H_o : \mu \ge 8300$

The alternative hypothesis is $H_a : \mu < 8300$

t = -3.34

p-value = P(t< -3.34) = 0.00041889

reject the null hypothesis

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 8300$

The sample mean is $\ = x = 8000$

The standard deviation is s = 440

The sample size is n = 24

The level of significance is $\alpha = 0.01$

The null hypothesis is $H_o : \mu \ge 8300$

The alternative hypothesis is $H_a : \mu < 8300$

The test statistic is mathematically evaluated as

$t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }$

=> $t = \frac{8000- 8300 }{ \frac{440}{\sqrt{24} } }$

=> t = -3.34

The p-value is obtained from the z -table ( reference calculator dot net ) , the value is

p-value = P(t< -3.34) = 0.00041889

Looking at the values of $p-value and \ \alpha$ we see that $p-value < \alpha$ Hence we reject the null hypothesis

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