Question

Conception about hypothesis test:

Q1. my professor said if the null hypothesis is true, then it is normal distribution but what does that mean? because sometimes we will reject the H0, does that mean if we reject it then it is not normal distribution?

Q2. sometimes we will have H0: u=30 something like that, but I don't understand as i was told that we don't know the population value; however u is the population value so i am confused. Plus, my professor said we need to use u to guess the true population value but why we assume u=30???

Here is my understanding: actually 30 may or may not be the true value but we assume it is true so we can do the hypothesis test???

Answer #1

1)

null hypothesis: distribution is normal

alternate hypothesis: distribution is not normal

so, yes, if we reject the Ho, then it means that distribution is not normal.

if we fail to reject Ho then we conclude that distribution is normal

2)

your concept is clear here, we just assume as in your example that true value ,u=30 is true

and in alternate hypothesis we take whether u >30 , u < 30 or u╪30.

Then we do hypothesis testing, to check which hypothesis to reject , and which to retain

based on that we make conclusions

conception:
for the null hypothesis test problem why we can use standard
normal distribution table?
by the central limited theorem and law of large number we have
that when n is getting large, then the sample distribution will be
normal distribution but it doesn't mean it is standard normal
distribution. But why we can still use the table to find the
value

conception clear up about sample variance
1. I heard that when the n is getting bigger, then the sample
variance will be zero. I don't understand here,variance means the
distance between the mean and the data value , in here does the
mean is sample mean or population mean???
2. if the sample variance is 0, then all the data value will be
same as the mean???
I am so confused, because how could that be possible, if we have...

1. The P-value of a test of the null hypothesis is
a. the probability the null hypothesis is true.
b. the probability the null hypothesis is false.
c. the probability, assuming the null hypothesis is false, that
the test statistic will take a value at least as extreme as that
actually observed.
d. the probability, assuming the null hypothesis is true, that
the test statistic will take a value at least as extreme as that
actually observed.
2. The P-value...

1.) Choose the true statement.
a.) If a null hypothesis is rejected for a test statistic at the
α=0.05 level, then at the α=0.01 level it would
never reject.
b.) If a null hypothesis is rejected for a test statistic at the
α=0.05 level, then at the α=0.01 level it would
always reject.
c.) If a null hypothesis is rejected for a test statistic at the
α=0.05 level, then at the α=0.01 level it may or
may not reject.
2.)...

Null hypothesis is the hypothesis that the researcher is trying
to disprove.It is denoted by H0
Alternative hypothesis is the hypothesis that the researcher is
trying to prove. It is reverse of null hypothesis and denoted by
Ha
Lets take an case where we need to test the claim which says the
mean weight of the student in class of 50 students exceeds 150
pounds
Here, the thing we are trying to prove is mean(u) >150
Thus, as discussed
Null...

I would like to test the null hypothesis that the population
mean is 50 versus the alternative that it is not 50. My sample size
is 6 and the sample mean is 38 with sample standard deviation of
16. At α = 0.05, I should:
Group of answer choices
Strongly reject the null hypothesis
Mildly reject the null hypothesis
Fail to reject the null hypothesis
Accept the alternative hypothesis
There is insufficient information to determine

Test the following claim. Identify the null hypothesis,
alternative hypothesis, test statistic, critical value(s),
conclusion about the null hypothesis, and final conclusion that
addresses the original claim. A manual states that in order to be
a hit, a song must be no longer than three minutes and thirty
seconds (or 210 seconds). A simple random sample of 50 current
hit songs results in a mean length of 250.0 sec. Assume the
population standard deviation of song lengths is 54.5 sec....

10. For a particular scenario, we wish to test the hypothesis
H0 : p = 0.52. For a sample of size
50, the sample proportion p̂ is 0.42. Compute the value of
the test statistic zobs. (Express your answer
as a decimal rounded to two decimal places.)
4. For a hypothesis test of
H0 : μ = 8
vs.
H0 : μ > 8,
the sample mean of the data is computed to be 8.24. The
population standard deviation is...

A hypothesis test is to be performed with a Null hypothesis
Ho: µ ≥ 15 and an alternative
hypothesis H1: µ <
15, the population standard deviation
is σ=2.0, the sample size is;
n=50, and the significance level is
α=0.025.
1- What is type l error?
2- What is the chance of making a type I error in the above
test?
3- What is a Type II error?
4- What value would the sample mean have to be less than to...

While testing a claim about population mean, if the value of the
population standard deviation σ is not known, then the distribution
we use:CHOOSE
Binomial Distribution
Standard Normal Distribution
None
Student's t-Distribution
With H0: p = 0.4, Ha: p < 0.4 , the test statistic is z = –
1.68. Using a 0.05 significance level, the P-value and the
conclusion about null hypothesis are:
0.0465; reject H0
0.093; fail to reject H0
0.9535; fail to reject H0
0.0465;...

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