Statistic question concerning hypothesis testing, please help me

Question

An economic advisor studies the effect of a policy decision on workers of the tourism

industry. He is essentially concerned with those who have been laid off from their work

because of the recession. He believes that an average of 50 works have been laid

off. He takes a random sample of 144 hotels from a distribution with unknown variance σ²

.For the observed sample of 144 hotels, the sample mean number of workers laid off is 55.2

and the sample standard deviation is 5.87. Perform an appropriate test of hypothesis to see if

the claim made by the economic advisor is acceptable (Test at the 5% level of significance).

Show every step of your work properly.

Answer 1

We need to use one sample T test here since the population variance is unknown.

Null hypothesis: µ = 50

Alternative hypothesis: µ is not equal to 50.

T test statistic = (55.2 - 50) / (5.87 / sqrt(144))

Then we can use a t-table or calculator to find the critical values or p-value to make a decision.

The two critical values for 5% test with degrees of freedom 144-1 = 143 are -1.976692 and +1.976692. If the above T test statistic is between these two values we cannot reject the null hypothesis. Otherwise we reject the null hypothesis.

Another way is to find the two-sided test p-value. If it's less than 5% we reject the null hypothesis.