For each of the following statements, identify whether the statement is true or false, and explain why. Please limit each response to no more than 3 sentences.
i) A p-value is the probability that the null hypothesis is false. ii) A chi-square test statistic can never be negative.
iii) If we reject the null hypothesis that a population proportion is equal to a specific value, then that specific value will not be contained in the associated confidence interval.
iv) If we reject the null hypothesis that the population mean is less than or equal to 1 at the 1% level of significance, then the lower bound of the associated 99% confidence interval will be greater than 1.
v) In simple linear regression, the fitted slope will always have the same sign (i.e. positive or negative) as the sample correlation.
i)false( it is probability of getting as or more exrteme test statisitc if null is true)
ii) true ( since chi square distribution start with 0 values , therefore it can not be negative)
iii) true (since confidence interval and hypothesis test gives the same result, therefore rejecting the null also means that confidence interval will not contain the given value)
iv) true (since confidence interval and hypothesis test gives the same result)
v) true (since both slope and corerlation coeffiicient sign represent the direction of linear trend)
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