Sinve the population is normally distributed and standart deviation is known, we can use Z-statistic
Null hypothesis: "u = 50"
Alternative hypothesis: "u < 50"
Test statistic: "Z={\\frac {(u-u{\\scriptscriptstyle 0})*\\sqrt{n}} {\u03c3}}", where u - sample mean, "u{\\scriptscriptstyle 0}" - claimed mean, n - sample size, σ - standard deviation
In our case: "Z={\\frac {(42-50)*\\sqrt{35}} {11.9}} = -3.98"
Due to the form of the alternative hypothesis, left-tailed test is appropriate
The critical value can be found as "P(N(0,1)<Z{\\scriptscriptstyle {cr}}) = \\alpha", where "\\alpha" - level of significance, "Z{\\scriptscriptstyle {cr}}" - critical value
In our case: "P(N(0,1)<Z{\\scriptscriptstyle {cr}}) = 0.01 \\to Z{\\scriptscriptstyle {cr}}" = - 2.33
Since "Z" < "Z{\\scriptscriptstyle {cr}}", we reject the null hypothesis.
There are statistically significant evidence that the population mean is now less than 50
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