Answer to Question #265102 in Statistics and Probability for Carl

Question

a) State the null and alternative hypothesis for a test to determine the validity of the claim

b) Identify left, right, or two-tailed test type

1. The average miniature horse is less than 34 inches at the shoulder. Tiny Equines claims that their miniature horses are an average of 3 inches less than the breed average.
2. Terrific Textiles claims that 45% to 55% of t-shirts sold in CO are red. 
3. Gas Hater Car Sales claims that 70% or more of the cars on the lot average more than 40 mpg. 
4. The 2011 average service time for Fast Fatz Burgers was 56 seconds. The store manager claims that the 2012 average is more than 5 seconds faster. 
5. Colorful Cavity Causers sells multi-colored candies by the bag. Each bag is claimed to average between 5.5 and 6.5 oz.
6. Aaron works for an electronics company, quality-testing batteries. The company claims a minimum of 5 hrs battery life.
7. The lessons in this Probability and Statistics text average 13 practice problems each.

Answer 1

1).

a) $H_0: \mu\ge31,\;H_a:\mu<31.$

b) Left-tailed.

2).

a) $H_0: \pi\le0.45 \cup \pi\ge0.55, \;H_a:0.45<\pi<0.55.$

b) Two-tailed.

3).

a) $H_0: \pi\ge 0.70,\; H_a:\pi<0.70.$

b) Left-tailed.

4).

a) $H_0: \mu \ge 51,\;H_a:\mu<51.$

b) Left-tailed.

5).

a) $H_0:\mu\; \le 5.5 \cup \mu \ge 6.5, \;H_a: 5.5<\mu<6.5.$

b) Two-tailed.

6).

a) $H_0:\mu\ge 5.5,\;H_a:\mu<5.5$.

b) Left-tailed.

7).

a) $H_0:\mu=13,\;H_a:\mu\ne13.$

b) Two-tailed.