A friend of yours (who is not taking any formal statisticalcourse) is doing a hypothesis test for a population proportion forhis final year project, described as follows:
A previous published study has shown that 25 percent of MalayArchipelago skulls from 150 AD, 200 BC, and 1850 BC had maximalskull breadth measurements of less than 132.25 mm. A new analysisis examining skulls from 4000 BC and 3300 BC (i.e. older skulls).60 total skulls have been examined from these 2 older time periods.Out of the 60 examined skulls, 24 skulls have maximal skull breadthmeasurements less than 132.25 mm. Your fellow friend believes theskull measurements for the older skulls will be different due tointerbreeding between groups that arrived in Malay Archipelagobetween these times and the newer times.

However, your friend is having trouble with some of theconcepts. Here is some part of his work. What mistakes can youfind? Help him to correct his WORK and his INTERPRETATIONS.

Let p be the population proportion of skulls with a maximalbreadth measurement of less than 132.25 mm.
𝐻0:𝑝̂=0.25 𝐻1:𝑝̂=2460=0.4
Assumption checking:
𝑛𝑝=60×0.25=15 and 𝑛(1−𝑝)=60×0.75=45. Minimum value is 15 and thisvalue is greater than or equal to 5.
Test statistic, 𝑡=0⋅25−0⋅4√0.25(0.75)60=−2.68
p-value = P(Z < −2.68) = 0.0037.
This means that the alternative hypothesis is true.
Therefore, the true value of null hypothesis must be 0.4 instead of0.25.