We would like to perform a twotailed hypothesis test about m

We would like to perform a two-tailed hypothesis test about mean at significance level of 0.05. The test statistic is already calculated for us, and the value is 2.1. We know that there are 25 observations in the random sample. The population is normally distributed, but the population standard deviation is unknown. What is the P-value? Do we have sufficient evidence to reject the null hypothesis? Why? Please show work.

Solution

We use t distirbution here because n < 30, and sigma is unknown.

We can calculate the P value using technology.

If you use Excel, you can type

=TDIST(your t, degrees of freedom, tails)

As t = 2.1, df = n - 1 =24, tails = 2,

=TDIST(2.1, 24, 2) yields

P = 0.046421502 [ANSWER]

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As P< 0 .05, we have sufficient evidence to reject the null hypothesis.