# (mu 1- mu 2) For two normal distributions Obtain the appropriate point estimator

Question
Normal distributions
$$\displaystyle{\left(\mu{1}-\mu{2}\right)}$$ For two normal distributions
Obtain the appropriate point estimator

2021-03-03
Step 1
Point Estimator :
Point estimators are functions that are used to find an approximate value of a population parameter from random samples of the population. They use the sample data of a population to calculate a point estimate or a statistic that serves as the best estimate of an unknown parameter of a population.
Most often, the existing methods of finding the parameters of large populations are unrealistic. For example, when finding the average age of kids attending kindergarten, it will be impossible to collect the exact age of every kindergarten kid in the world. Instead, a statistician can use the point estimator to make an estimate of the population parameter.
Step 2
$$\displaystyle\mu_{{1}}−\mu_{{2}}-\mu_{{1}}$$ : mean of Manufacturer 1
$$\displaystyle\mu_{{2}}$$ : mean of Manufacturer 2
$$\displaystyle\mu_{{1}}-\mu_{{2}}$$ : mean difference

### Relevant Questions

Select all that apply. We show that our sample statistics have (at minimum) a somewhat normal distribution because
this allows us to use t and z critical values.
this allows us to use t and z tables for probabilities.
this tells us that our sampling is appropriate.
normal distributions are cool and that's all we talk about in this class.
Let two independent random samples, each of size 10, from two normal distributions $$\displaystyle{N}{\left(\mu_{{1}},\sigma_{{2}}\right)}{\quad\text{and}\quad}{N}{\left(\mu_{{2}},\sigma_{{2}}\right)}$$ yield $$\displaystyle{x}={4.8},{{s}_{{1}}^{{2}}}$$
$$\displaystyle={8.64},{y}={5.6},{{s}_{{2}}^{{2}}}$$
= 7.88.
Find a 95% confidence interval for $$\displaystyle\mu_{{1}}−\mu_{{2}}$$.
The manager of the store in the preceding exercise calculated the residual for each point in the scatterplot and made a dotplot of the residuals.
The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of$22.92.
The middle 95% of residuals should be between which two values? Use this information to give an interval of plausible values for the weekly sales revenue if 5 linear feet are allocated to the store's brand of men's grooming products.
There is a direct relationship between the chi-square and the standard normal distributions, whereby the square root of each chi-square statistic is mathematically equal to the corresponding z statistic at significance level $$\displaystyle\alpha$$.
1.True
2.False
Answer true or false to each statement.
a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.
b. Two normal distributions that have the same standard deviation have the same spread, regardless of the relationship between their means.
When we want to test a claim about two population means, most of the time we do not know the population standard deviations, and we assume they are not equal. When this is the case, which of the following is/are not true?
-The samples are dependent
-The two populations have to have uniform distributions
-Both samples are simple random samples
-Either the two sample sizes are large or both samples come from populations having normal distributions or both of these conditions satisfied.