Question

In: Statistics and Probability

A company claims that 9 out of 10 doctors (i.e. 90%) recommend its brand of cough...

A company claims that 9 out of 10 doctors (i.e. 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of 200 doctors was chosen which results in 160 who indicate that they recommend this cough syrup. Find the standardized test statistic, z. Round to two decimal places.

Expert Solution

Let's choose level of significance = 5% ( since it is not given )

We have our hypothesis defined as :

Null hypothesis H0: p >= 0.90 i.e actual proportion is great than or equal to 0.9

Alternative hypothesis H1: p < 0.90 i.e. actual proportion is less than 0.9

Therefore, this is a left tailed left.

The one proportion z- test is given by :

where,

z = Test statistics
n = Sample size = 200
po = Null hypothesized value = 0.9
= Observed proportion = 160/200 = 0.8

z = = = - 4.716

The z- score at 5% level of significance for left tailed test is calculated as follows :

1. Calculate 0.5 - 0.05 = 0.45 ( 0.05 is the level of significance )

2. Spot value closest to 0.45 in the z- table.

3. Look for the column and row label, put the column label at the second decimal point of row label and put minus sign.

here, Row label = 1.6 and column label = 0.05

So, we have our z - score = - 1.65

Now, since our Z_calculated < Z _critical i.e -4.716 < -1.65 , we reject out null hypothesis and accept the alternate hypothesis.

Therefore, we accept the alternate hypothesis that the actual proportion is less than 0.9

orchestra answered 1 year ago

A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their...

A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of doctors was taken. Suppose the test statistic is zequalsnegative 2.23. Can we conclude that Upper H 0 should be rejected at the a right parenthesis alpha equals 0.10 comma b right parenthesis alpha equals 0.05...

A pharmaceutical industry survey claims that 9 out of 10 doctors recommend aspirin for their patients...

A pharmaceutical industry survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test the claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. What is the value of the test statistic used in evaluating this claim? Include 2 decimal places in your answer.

A popular toothpaste brand claims that four out of five (or eighty percent) of dentists recommend...

A popular toothpaste brand claims that four out of five (or eighty percent) of dentists recommend their brand. 1. You randomly select 35 dentists. Calculate the probability that the sample proportion is between 74 percent and 88 percent. 2. Comment on the appropriateness of the sample size.

2. Insurance Company An insurance company states that 90% of its claims are settled within 30...

2. Insurance Company An insurance company states that 90% of its claims are settled within 30 days. A consumer group selected a random sample of 75 of the company's claims to test this statement. If the consumer group found that 55 of the claims were settled within 30 days, do they have sufficient reason to support their contention that fewer than 90% of the claims are settled within 30 days? Use 0.05 level of significance. Hint: We are testing for...

The State Farm Insurance Company boasts that 90% of its customers who make claims are satisfied...

The State Farm Insurance Company boasts that 90% of its customers who make claims are satisfied with the service. To check the accuracy of this declaration, the company conducts a survey wherein customers are asked whether they were satisfied with the quality of service. 153 were satisfied and 24 were not satisfied. Can we infer at the 5% level of significance that the satisfaction rate is less than 90%? (Use 4 decimal places in your initial work for this problem.)...

3. A company claims that its medicine, Brand A, provides faster pain relief than another company’s...

3. A company claims that its medicine, Brand A, provides faster pain relief than another company’s medicine, Brand B. A researcher tested both brands of medicine on two groups of randomly selected patients. The results of the medical tests are given in the following table. The mean and standard deviation of relief times are in minutes. Brand Sample Size Mean Relief Times Standard Deviation of Relief Times Brand A 25 44 11 Brand B 22 49 9 (a) Define...

Shipping time. An internet company claims that 90% of its orders are shipped within two days. Suppose...

Shipping time. An internet company claims that 90% of its orders are shipped within two days. Suppose that last month they received 4000 orders. A consumer group questioning the claim took a random sample of 200 orders and found that 168 were shipped within 2 days. Is this strong enough evidence to conclude that less than 90% of all orders received were shipped within two days? Use a significance level of 5%. Then, qualify your findings to a range of percentages. A) Identify problem type: mean...

Of the 35 doctors offices within a 10 mile radius, 9 have only one physician on...

Of the 35 doctors offices within a 10 mile radius, 9 have only one physician on staff, 15 have two on staff, 6 have three physicians on staff, and 5 have four physicians on staff. A physician is chosen at random. What is the probability that this person is from a doctors office with 2 physicians on staff?

Trydint" bubble-gum company claims that 8 out of 10 people prefer their gum to "Eklypse". Test...

Trydint" bubble-gum company claims that 8 out of 10 people prefer their gum to "Eklypse". Test their claim at the 95 confidence level. The null and alternative hypothesis in symbols would be: A)H0:p≤0.8H H1:p>0.8 B)H0:p≥0.8 H1:p<0.8 C)H0:p=0.8 H1:p≠0.8 D)H0:μ=0.8 H1:μ≠0.8 E)H0:μ≤0.8 H1:μ>0.8 F)H0:μ≥0.8 H1:μ<0.8 The null hypothesis in words would be: A)The proportion of all people that prefer Trydint gum is 0.8 B)The average of people that prefer Trydint gum is not 0.8. C)The proportion of all people that prefer...

"Trydint" bubble-gum company claims that 5 out of 10 people prefer their gum to "Eklypse". Test...

"Trydint" bubble-gum company claims that 5 out of 10 people prefer their gum to "Eklypse". Test their claim at the 90 confidence level. The null and alternative hypothesis in symbols would be: H0:μ≤0.5 H1:μ>0.5 H0:p=0.5 H1:p≠0.5 H0:μ≥0.5 H1:μ<0.5 H0:p≤0.5 H1:p>0.5 H0:μ=0.5 H1:μ≠0.5 H0:p≥0.5 H1:p<0.5 The null hypothesis in words would be: The proportion of all people that prefer Trydint gum is less than 0.5. The proportion of all people that prefer Trydint gum is 0.5 The proportion of people in...