Question

Hypothesis testing - A car insurance company claims that it will save new customers 15% of what they pay for their current plans with other insurance companies. In a random sample of 30 new customers, the average amount saved was 8% with a standard deviation of 2%.

Answer 1

this needs more information. whats the question

Answer 2

I'm assuming you're using the default 5% significance level


Find the z-score to get

z = (xbar - mu)/(sigma/sqrt(n))

z = (0.08 - 0.15)/(0.02/sqrt(30))

z = -19.1702895


Since this standard normal z score is definitely outside the interval from -1.96 to 1.96, this means that this score lies in the rejection region. So you would reject the null hypothesis (that mu = 0.15) and you would be forced to accept the alternative hypothesis (that mu doesn't equal 0.15)

Answer 3

@jim_thompson5910 can you explain the steps to me please ?

Answer 4

what is your question

Answer 5

we're told that "A car insurance company claims that it will save new customers 15%", so the company claims that the average savings is 15% or 0.15

therefore, the population mean mu is

mu = 0.15

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because we have a random sample of 30 people, we know that n = 30

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it then says that for that sample, the "average amount saved was 8%", so the sample mean xbar is

xbar = 0.08

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the standard deviation is

sigma = 0.02

since it says " with a standard deviation of 2%"

Answer 6

So that sets up all the given variables and their corresponding values

Answer 7

you then take the raw score of 0.08 and convert it to a z-score like so


z = (xbar - mu)/(sigma/sqrt(n))

z = (0.08 - 0.15)/(0.02/sqrt(30))

z = -19.1702895

Answer 8

so i take the absolute value of that and since | -19 | = 19
19 > 1.96 i reject the null hypothesis with 95% certainty right ?

Answer 9

The two hypotheses are

Null Hypothesis:

Ho: mu = 0.15

Alternative Hypothesis

Ha: mu =/= 0.15


So that means we're doing a two tailed test. At the default significance level of 5%, the area in the tails is 0.05/2 = 0.025

You would then use a calculator or a table to find that P(Z < -1.96) = 0.025 or P(Z > 1.96) = 0.025

This means that the acceptance region is from z = -1.96 to z = 1.96

If you get a z-score in this region, then you fail to reject the null hypothesis (and must accept it). If not, then you reject the null hypothesis

Answer 10

So because we got a z-score that's outside the interval from z = -1.96 to z = 1.96, we reject the null hypothesis

Answer 11

thank you so much ! i appreciate it

Answer 12

you're welcome

Answer 13

and the population mean x bar is equal to population mean