A credit card company claims that the mean credit card debt for individuals is greater than $5,000. You want to test this claim. You find that a random sample of 35 cardholders has a mean credit card balance of $5,160 and a standard deviation of $625. At α=0.05, can you support the claim? Assume the population is normally distributed. a) Write the claim mathematically and identify H o and H a?(b) Find the critical value(s) and identify the rejection region(s).What is(are) the critical value(s)?(c) Find the standardized test statistic t.(e) Interpret the decision in the context of the original claim.

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step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: