Question

A hospital director is told that 70% of the treated patients are insured. The director wants to test the claim that the percentage of insured patients is more than the expected percentage. A sample of 200 patients found that 150 were insured. At the 0.05 level, is there enough evidence to support the director's claim?

Step 1 of 7: State the null and alternative hypotheses.

Step 2 of 7: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 7: Specify if the test is one-tailed or two-tailed.

Step 4 of 7: Determine the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 7: Identify the value of the level of significance.

Step 6 of 7: Make the decision to reject or fail to reject the null hypothesis.

Step 7 of 7: State the conclusion of the hypothesis test.

Answer 1

i am using minitab to solve the problem.

steps :-

stat $1596051422659_blob.png$basic statistics $1596051422687_blob.png$1 proportion $1596051422882_blob.png$ select summarized data from the drop down menu $1596051422895_blob.png$in number of events type 150 , in number of trials type 200 $1596051422947_blob.png$ tick perform hypothesized test $1596051422885_blob.png$ in hypothesized proportion type 0.70 $1596051422912_blob.png$options $1596051422924_blob.png$ in confidence level type 95 $1596051422903_blob.png$ select the alternative hypothesis as proportion > hypothesized proportion $1596051422911_blob.png$ in method select normal approximation $1596051422914_blob.png$ok$1596051422907_blob.png$ok.

to round off any value to needed decimal places :-

right click on the value $1596051485374_blob.png$decimal places $1596051485429_blob.png$ select the needed place(here, we will select 4 in p value )

*** SOLUTION ***

1).hypothesis:-

$H_{0}:p=0.70$

$H_{1}:p>0.70$ [ claim ]

2). the test statistic (z) = 1.54

3). this is a one-tailed (right tailed) test.

4).the P-value of the test statistic = 0.0614

5).the value of the level of significance (alpha) = 0.05

6). decision: fail to reject the null hypothesis.

[ p value = 0.0614 > 0.05 (alpha) ]

7). the conclusion of the hypothesis test :-

there is not enough evidence to support the claim that the percentage of insured patients is more than the expected percentage.

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