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scZoUnD [109]
2 years ago
6

The null and alternate hypotheses are: H0: ????1 ???? ????2 H1: ????1 ???? ????2 A random sample of 15 observations from the fir

st population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard devi- ation of 15. At the .10 significance level, is there a difference in the population means?
Mathematics
1 answer:
bija089 [108]2 years ago
5 0

Answer:

t=\frac{(350-342)-0}{\sqrt{\frac{12^2}{15}+\frac{15^2}{17}}}}=1.674  

The degreess of freedom are given by:

df = 15+12-2 =25

Now we can calculate the p value with the following probability:

p_v =2*P(t_{25}>1.674)=0.107  

For this case since the p value is higher than the significance level we can FAIL to reject the null hypothesis and we can conclude that the true means are NOT significantly different at 10% of significance.

Step-by-step explanation:

Information provided

\bar X_{1}=350 represent the mean for sample 1  

\bar X_{2}=342 represent the mean for sample 2  

s_{1}=12 represent the sample standard deviation for 1  

s_{2}=15 represent the sample standard deviation for 2  

n_{1}=15 sample size for the group 2  

n_{2}=17 sample size for the group 2  

\alpha=0.1 Significance level provided

t would represent the statistic

Hypothesis to test

We want to verify if the true means for this case are significantly different, the system of hypothesis would be:  

Null hypothesis:\mu_{1}-\mu_{2}=0  

Alternative hypothesis:\mu_{1} - \mu_{2}\neq 0  

The statistic is given by:

t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)  

And the degrees of freedom are given by df=n_1 +n_2 -2=15+17-2=30  

Replacing the info given we got:

t=\frac{(350-342)-0}{\sqrt{\frac{12^2}{15}+\frac{15^2}{17}}}}=1.674  

The degreess of freedom are given by:

df = 15+12-2 =25

Now we can calculate the p value with the following probability:

p_v =2*P(t_{25}>1.674)=0.107  

For this case since the p value is higher than the significance level we can FAIL to reject the null hypothesis and we can conclude that the true means are NOT significantly different at 10% of significance.

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