Solution:
Here, we have to use one sample z test for the population mean.
The null and alternative hypotheses are given as below:
H0: µ = 260.7
H1: µ > 260.7
This hypothesis test is a right-tailed (upper-tailed) test.
The test statistic formula is given as below:
Z = (x̄ - µ)/[σ/sqrt(n)]
From given data, we have
µ = 260.7
x̄ = 293
σ = 155
n = 60
α = 0.1
Critical value = 1.2816
(by using z-table or excel)
Z = (293 - 260.7)/[ 155/sqrt(60)]
Z = 1.6142
Test statistic = 1.6142
Test statistic > Critical value
So, we reject the null hypothesis
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