Question

It is known that 1 year old dogs have a mean gain in weight of 1.0 pound per month with a standard deviation of 0.40 pound. A special diet supplement, Helthpup, is given to a rando sample of 36, 1-year-old dogs for a month; their mean gain in weight is 2.15 pounds. At the 0.01 level of significance, does helthpup affect weight gain in 1-year-old dogs? (a) What is the research problem? (b) State null and alternative hypothesis (c) Is this one or two tail test? why? (d) what is the critical value? (e) what is the decision rule? (f) calculate the statistic (g) what is your decision regarding null hypothesis and why? (h)interpretation of the results?

Answer 1

GIVEN:

Population standard deviation pounds

Hypothesized value pound

Sample size of 1 year old dogs

Sample mean gain in weight pounds

(a) RESEARCH PROBLEM:

The given problem is to test whether the special diet supplement, Helthpup, affect the weight gain in 1 year old dogs (That is, whether the true mean weight gain in 1 year old dogs is less than 1.0 pound per month). Thus we use "One sample z test" to test this claim.

(b) HYPOTHESIS:

The hypothesis is given by,

(That is, the true mean weight gain in 1 year old dogs is greater than or equal to 1.0 pound per month. In other words, the special diet supplement, Helthpup, does not affect the weight gain in 1 year old dogs.)

(That is, the true mean weight gain in 1 year old dogs is less than 1.0 pound per month. In other words, the special diet supplement, Helthpup, affect the weight gain in 1 year old dogs.)

(c) The given problem is a one tailed (left tailed) test since the alternative hypothesis is .

LEVEL OF SIGNIFICANCE:

(d) CRITICAL VALUE:

The left tailed (since ) z critical value at significance level is .

(e) DECISION RULE:

(f) TEST STATISTIC:

which follows standard normal distribution.

CALCULATION:

  

  

(g) DECISION REGARDING NULL HYPOTHESIS:

Since the calculated z test statistic (17.25) is greater than the z critical value (-2.33), we fail to reject null hypothesis.

(h) CONCLUSION:

Since the calculated z test statistic (17.25) is greater than the z critical value (-2.33), we fail to reject the null hypothesis and conclude that the true mean weight gain in 1 year old dogs is greater than or equal to 1.0 pound per month. In other words, the special diet supplement, Helthpup, does not affect the weight gain in 1 year old dogs.