A storé is offering a 20% discount on all items. Write an equation for the relationship between the discount price of an item, d
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a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.
b. z=1.24. No, it can not be concluded that the population mean is greater than 50.
c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.
Step-by-step explanation:
We have a hypothesis test for the mean, with the hypothesis:
The sample size is n=55 and the population standard deviation is 6.
The significance level is 0.05.
We can calculate the standard error as:
For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.
a. If the sample mean is M=52.5, the test statistic is:
The null hypothesis is rejected, as z>zc and falls in the rejection region.
b. If the sample mean is M=51, the test statistic is:
The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.
c. If the sample mean is M=51.8, the test statistic is:
The null hypothesis is rejected, as z>zc and falls in the rejection region.
For this case we have:
Let x be the variable that belongs to the real numbers. Then, all reals less than 70 can be expressed as:
The tip of the inequality is directed to the real numbers, since they tell us that they are less than 70, for 70 the inequality remains open.
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