Question

1b)The value of the standardized test statistic is:

In the past, a company used to produce 40 tons of a certain food per day on average. Now, using a new technology, the mean daily yield of the food for a random sample of 25 days of production is 45 tons with a standard deviation of 5 tons. Assume that the daily yield of this food is normally distributed. Set up the null and the alternative hypothesis to test whether the new technology has increased the mean daily yield. O Ho: M = 40 versus Ha:M + 40. O Ho: Mi < 45 versus Hail> 45. O Hoil < 40 versus Haill> 40. O Hoill> 45 versus Haill< 45. O Ho:ll> 40 versus Ha:M<40.

Group of answer choices

a) 1.00

b) 5.00

c) None of the above

d) -5.00

e) -1.00

1c)Find the rejection region and state your conclusion at \alphaα = 0.05.

Group of answer choices

a) Reject region: t < -1.711; Decision: Fail to reject H0

b) Reject region: z > 1.645; Decision: Reject H0

c) Reject region: t < -2.064 or z > 2.064; Decision: Reject H0

d) Reject region: t > 1.711; Decision: Reject H0

e) Reject region: z < -1.96 or z > 1.96; Decision: Fail to reject H0

Answer 1

a) Option-C) H₀ : µ < 40 versus H₁ : µ > 40

b) Test statistic $=\frac{\bar{X}-\mu}{s/\sqrt{n}}$

                        $=\frac{45-40}{5/\sqrt{25}}$

                        = 5

Option-B) 5

c) t_0.05,24 = 1.711

Option-D) Reject region: t > 1.711; Decision: Reject H0