The correct option is C which is The z-statistic is 3.32, so the null hypothesis should be rejected. One can reject the null hypothesis.
When there are two possibilities then we calculate the null hypothesis if the hypothesis is true hypothesis is accepted if it is
To conduct a hypothesis test for the above situation. We define the null hypothesis and the alternative hypothesis.
The null hypothesis is the claim that the average commute time to downtown is 20 minutes while the alternative hypothesis is a contradiction of the null hypothesis which is that the average commute time to downtown is not 20 minutes.
i.e. H0: μ = 20 and H1: μ ≠ 20.
The z-statistics is given by (sample mean - hypothesized mean) divided by (standard deviation divided by the square root of the sample size).
i.e.
[tex]z= \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
x = 26, [tex]\mu[/tex] = 20, [tex]\sigma[/tex] = 7 and n = 15 putting the values in the question we will get the z-score value.
[tex]z = \dfrac{26-20}{\dfrac{7}{\sqrt15}}[/tex]
z = 6 / 1.807
z = 3.32
Therefore, the z-statistic is 3.32, so the null hypothesis should be rejected. Because the calculated value of z (3.32) is greater than the table value of z (1.96).
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