Some areas which i don't understand for hypothesis testing in Qbank concerning, conclusion, understand, hypothesis

sabre

Hi, i have a question from qbank which i need some help.


From the question, it states that 'test of a hypothesis concerning whether a population mean is zero'
Below is my conclusion for the hypothesis is:

H0 not equal to zero
Ha is equal to zero (my alternative hypothesis is equal to zero bcos he is testing whether the population is zero)

My 1st question: is my hypothesis as shown above correct?

Next my second question is what does it mean by: "population mean is significantly different from zero". My interpretation is the population is not equal to zero.

Thanks for the help and guidance

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In a two-tailed test of a hypothesis concerning whether a population mean is zero, Jack Olson computes a t-statistic of 2.7 based on a sample of 20 observations where the distribution is normal. If a 5% significance level is chosen, Olson should:

A) reject the null hypothesis and conclude that the population mean is not significantly different from zero.

B) reject the null hypothesis and conclude that the population mean is significantly different from zero.

C) fail to reject the null hypothesis that the population mean is not significantly different from zero.


Your answer: A was incorrect. The correct answer was B) reject the null hypothesis and conclude that the population mean is significantly different from zero.

At a 5% significance level, the critical t-statistic using the Student’s t-distribution table for a two-tailed test and 19 degrees of freedom (sample size of 20 less 1) is

Matori

Thanks for the explanation

agulani

The basic premise of hypothesis testing is that you do not know the value of a parameter of a population. You want to test that it is not some value, say 0 in your example above. You test it by taking a sample of values and finding their mean. Depending on what you get, you can say whether the population mean has a 95% probability of being 0 or 90% depending on significance level chosen. (THink of it this way, if sample mean is very close to 0, there is a good chance that pop mean is 0).

Even if pop mean is 0, the sample mean you get may not be 0 since it doesnt include all members of the population. But it may be so small that it is not significantly different from 0 (statistically speaking)







You think that the population mean is something other than 0 so you state
Ho - mean = 0
Ha - mean not equal to 0