State whether the null hypothesis should be rejected on the

Question

1. Using the Z table to find the critical value(s) for each

a)  α = 0.04, left-tailed test                  b)  α = 0.05, two-tailed test    c)   α = 0.005, right-tailed test

2. Write down the hypothesis for each of the following:

a)  An additive is claimed to improve automotive battery life (mean: 3 years)

b)  Robot can reduce car assembly manufacturing defect to less than 20 C/100

c)  Music is known to affect the test score (mean: 80) but do not know better or worse

e)  Good job opportunity affect the college student age (ave: 25 yrs)

3. a) Walking (µ = 5 000 steps/day and σ = 600 steps/day) is shown to improve health.  A group of 40 health-conscious employees take average of 5430 steps/day.  At α = 0.05 can it be concluded that they walked more than the mean?

 b) US Senators (µ = 60 yrs and population σ = 6.5 yrs), while state senators may be different.

A random sample of 40 from various states has an average of 55 years.

At  α = 0.05 is there sufficient evidence that state senators are younger on average?

 c) State whether the null hypothesis should be rejected on the basis of given P value

      I)  P value = 0.258  α = 0.05, one-tailed test     II)  P value = 0.0684  α = 0.10, two-tailed test

 d) Home prices in two cities were compared to see if there is a difference at α = 0.01.
                   Scott          X₁ bar = $93,430,   σ₁= $5602,   n₁  = 35;                                                        
                 Ligonier       X₂ bar = $98,043,   σ₂ = $4731,   n₂ = 40
       Is there enough evidence to reject the claim that the average price is the same?

4. PGA Golf Scores At a recent PGA tournament (the Honda Classic at Palm Beach Gardens, Florida) the following scores were posted for eight randomly selected golfers for two consecutive days.

(a) At α = 0.05, is there evidence of a difference in mean scores for the two days?

(b) Find the 95% confidence interval of the difference in the means.

Golfer	1	2	3	4	5	6	7	8
Thursday	67	65	68	68	68	70	69	70
Friday	68	70	69	71	72	69	70	70

5. Prices of Low-Calorie Foods The average price of a sample of 12 bottles of diet salad dressing taken from different stores is $1.43. The standard deviation is $0.09. The average price of a sample of 16 low-calorie frozen desserts is $1.03. The standard deviation is $0.10.

(a) At α = 0.01, is there a significant difference in price?

(b) Find the 99% confidence interval of the difference in the means.