Question

Various temperature measurements are recorded at different times for a particular city. The mean of 20 o C is obtained from a sample of 32 temperatures. If we know that historically for this city the mean daily temperature is μ = 22 o C and that σ = 3.5 o C , test the claim that the city is actually colder than now than previously believed. Use α = .01 for this problem. Round all values to three decimal places where necessary. State your null and alternative hypothesese. Use \mu for μ . h 0 : h 1 : What is the correct test to use for this hypothesis test? Select an answer What is the P-value for this test? Be sure to write as a decimal and not in scientific notation if it applies. What is your decision? Select an answer Clearly state your conclussion in complete sentences.

Answer 1

Solution :

= 22

= 20

= 3.5

n = 32

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 22

Ha :    22

Test statistic = z

= ( - ) / / n

= (20-22) / 3.5 / 32

= -3.23

Test statistic = z = -3.23

P(z < -3.23 ) =  0.0006

P-value = 2 * 0.0006 =0.0012

= 0.01

P-value <

0.0012 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that