Question

the thermostat in your lecture room is set at 72°F, but you think the thermostat isn’t working well. On seven randomly selected days, you sit in the same seat near the thermostat and measure the temperature. Your measurements (in degrees Fahrenheit) are 71, 73, 69, 68, 69, 70, and 71. For the hypothesis: H₀: µ = 72°    and   H_A: µ ¹ 72°, what is the p-value and conclusion for your test using a 0.05 significance level?

With explanation of work

Answer 1

Ho : = 72 Vs HA : 72

Test statistic t

t = (xbar - )/(s/√n)

t = ( 70.14-72)/(1.68/√7)

t = -2.93

Degrees of freedom = n -1 = 7 -1 = 6

p-value for t= -2.93 with d.f = 6 , two tailed test

p-value = 2*P( t < -2.93) d.f = 6

p-value = 0.0263

Decision rule : if p-value < a we reject the null hypothesis otherwise we fail to reject the null hypothesis

Given level of significance a =0.05

Our p-value = 0.0263 < 0.05

Conclusion : Reject the null hypothesis Ho . There is sufficient evidence to support the claim that thermostat not working well.