Question

A nationwide survey of working adults indicates that out of 100 adults, 50 of them are satisfied with their jobs. The president of a large company believes that more than this number of employees at his company are satisfies with their jobs. To test his belief, he surveys a random sample of 100 employees, and 59 of them report that they are satisfied with their jobs. Do you support president’s statement about the employees satisfaction? (Use α = 0.05 level of significance.)

(a) H0 :

(b) Ha :

(c) Test Statistic:

(d) Decision:

(e) Conclusion:

(f) Compute a 95% lower bound for population proportion p. Interpret your result.

Answer 1

Proportion (p0) = 0.5

Total number of sample (n) = 100

number of favourable events (X) = 59

We are interested in testing the hypothesis

c)

Since P-value of a two tailed test is equal to

P = (1-0.9640696808870742)

P = 0.03590000000000004

d) Since, the test is two-tail test at \alpha = 0.05

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 1.64

e) The statistic value, 1.8 is greater than the critical value 1.64. Hence, reject the null hypothesis.

f) Sample proportion = 0.59

Sample size (n) = 100

Confidence interval(in %) = 95

z @ 95% = 1.96

Since we know that

Required confidence interval = (0.59-0.0964, 0.59+0.0964)

Required confidence interval = (0.4936, 0.6864)

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