A national newspaper reported that the state with the longest mean life span is

Question

A national newspaper reported that the state with the longest mean life span is Hawaii, where the population mean life span is 76 years. A random sample of 20 obituary notices in the Honolulu Advertizer gave the following information about life span (in years) of Honolulu residents.

72 68 81 93 56 19 78 94 83 84

77 69 85 97 75 71 86 47 66 27

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x-bar = ______ yr

s = ______ yr

(ii) Assuming that life span in Honolulu is approximately normally distributed, does this information indicate that the population mean life span for Honolulu residents is less than 76 years? Use a 10% level of significance.

(a) What is the level of significance? _____________________

State the null and alternate hypotheses. (Multiple Choice)

-H0: = 76 yr; H1: > 76 yr

-H0: > 76 yr; H1: = 76 yr

-H0: = 76 yr; H1: 76 yr

-H0: = 76 yr; H1: < 76 yr

-H0: < 76 yr; H1: = 76 yr

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. (Multiple Choice)

-The standard normal, since we assume that x has a normal distribution and is unknown.

-The standard normal, since we assume that x has a normal distribution and is known.

-The Student's t, since we assume that x has a normal distribution and is unknown.

-The Student's t, since we assume that x has a normal distribution and is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.) __________________

(c) Find the P-value. (Round your answer to four decimal places.) _________________________

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? (Multiple Choice)

-At the = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.

-At the = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.

-At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

-At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application. (Multiple Choice)

-There is sufficient evidence at the 0.10 level to conlcude that the population mean life span of Honolulu residents is less than 76 years.

-There is insufficient evidence at the 0.10 level to conclude that the population mean life span of Honolulu residents is less than 76 years.

Explanation / Answer

(i) From excel calculations,

Mean = 71.14

Standard deviation = 20.13

first we need to use 10% significance level for N=20

We use students t test since N<30

degrees of freedom = N-1= 19

critical t value = 1.725 from t-table

Null Hypothesis:

= 76 yr;

Alternate Hypothesis:

Does is indicate that the population mean life span for Honolulu residents is less than 76 years

< 76 yr

T-Test

t= (x-u)*sqrt(n-1)/s

=(76-71.14)*sqrt(19)/20.12

=0.245

p-value for 0.1 level < p-value 0.595

hence less significant

At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.