## To test Upper H 0 : mu equals 107 versus Upper H 1 : mu not equals 107 a simple random sample of size nequals35 is obtained. Complete parts

To test Upper H 0 : mu equals 107 versus Upper H 1 : mu not equals 107 a simple random sample of size nequals35 is obtained. Complete parts a through e below. LOADING… Click here to view the t-Distribution Area in Right Tail.Several years ago, the mean height of women 20 years of age or older was 63.7 inches. Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 64.1 inches. (a) State the appropriate null and alternative hypotheses to assess whether women are taller today. (b) Suppose the P-value for this test is 0.17. Explain what this value represents. (c) Write a conclusion for this hypothesis test assuming an alphaequals0.05 level of significance.

## Answers ( )

Answer:

a)

H0: μ = 63.7

Ha: μ ≠ 63.7

b) If the P-value for this teat is 0.17, this is a relatively high p-value. A higher p-value means that there is stronger evidence in favor of the null hypothesis while a smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

c)

Conclusion:

we would FAIL to REJECT the null hypothesis. That is there is no sufficient evidence to state that the mean height of women 20 years of age or older is not equal to 63.7 inches. Null hypothesis is still valid.

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For this case, Let μ represent the mean height of women 20 years of age or older.

The null hypothesis is that the mean height of women 20 years of age or older is equal to 63.7 inches.

H0: μ = 63.7

The alternative hypothesis is that the mean height of women 20 years of age or older is not equal to 63.7 inches.

Ha: μ ≠ 63.7

b) If the P-value for this teat is 0.17, this is a relatively high p-value. A higher p-value means that there is stronger evidence in favor of the null hypothesis while a smaller p-value means that there is stronger evidence in favor of the alternative hypothesis. Assuming testing at 5% significance level, the P-value is higher than 0.05, which means we would FAIL to reject the null hypothesis. That is there is no sufficient evidence to state that the mean height of women 20 years of age or older is not equal to 63.7 inches.

c)

Rule

If;

P-value > significance level — accept Null hypothesis

P-value < significance level — reject Null hypothesis

Conclusion:

we would FAIL to REJECT the null hypothesis. That is there is no sufficient evidence to state that the mean height of women 20 years of age or older is not equal to 63.7 inches. Null hypothesis is still valid.