`consider the population of a small town that grows according to the explicit rule Pn = 3500 + 18n

Kindly check explanation

Step-by-step explanation:

H0 : μ ≥ 402

H1 : μ < 402

Test statistic :

n = 23

Sample Mean, x = 400

Variance = 900

σ = sqrt(900) = 30

Test statistic = (x - μ) ÷ σ/sqrt(n)

Test statistic = (400 - 402) ÷ 30/sqrt(23)

Test statistic = - 2 / 6.2554324

Test statistic = - 0.3197221

Test statistic = - 0.3197

Critical value :

Using the Tcritical value calculator

Tcrit; α = 0.025, df = n - 1 = 23 - 1 = 22

Tcritical = 2.074

Reject Null : if Test statistic ≤ Tcritical (left tail test)

Since ;

Test statistic ≤ Tcritical ; We reject the Null