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didi2096
14.04.2020 •
Mathematics
You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.34 with a standard deviation of 0.456. You sample 25 day students, and the sample mean GPA is 2.59 with a standard deviation of 0.482. Test the claim using a 10% level of significance. Assume the sample standard deviations are unequal and that GPAs are normally distributed.
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Ответ:
If we compare the p value and the significance level given
we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the two means are different at 10% of significance.
Step-by-step explanation:
Data given and notation
t would represent the statistic (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the two means are equal or no, the system of hypothesis would be:
Null hypothesis:![\mu_{A} = \mu_{B}](/tpl/images/0598/2701/49a31.png)
Alternative hypothesis:![\mu_{A} \neq \mu_{B}](/tpl/images/0598/2701/32e05.png)
If we analyze the size for the samples both are <= than 30 and we don't know the population deviations, for this case is better apply a t test to compare means, and the statistic is given by:
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
Conclusion
If we compare the p value and the significance level given
we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the two means are different at 10% of significance.
Ответ:
When we round a decimal number to tenth , it means we need to round this to one decimal place.
Notice here next number after the first number 3 is 8. Since 8 is more than 5. So, 3 will increase by 1. So, it become 3+1=4.
Hence we can round 0.38 as 0.4 to tenth.