Question

In: Statistics and Probability

In the 1990s, it was generally believed that genetic abnormalities affected about 8% of a large...

In the 1990s, it was generally believed that genetic abnormalities affected about 8% of a large nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities, which could have important implications for health insurance companies. A recent study examined 369 randomly selected children and found that 40 of them showed signs of a genetic abnormality.

(a) Which hypotheses should be used to test if the proportion of genetic abnormalities has increased in recent years?

H₀: p = 0.08 vs. H_a: p > 0.08

H₀: p = 0.1084 vs. H_a: p > 0.1084

H₀: p = 0.08 vs. H_a: p < 0.08

H₀: p = 0.1084 vs. H_a: p ≠ 0.1084

H₀: p = 0.08 vs. H_a: p ≠ 0.08

H₀: p = 0.1084 vs. H_a: p < 0.1084

(b) Are the conditions met for doing the hypothesis test?

None of the conditions are met.

The children taking part in the study were independent of each other.

The sample was randomly chosen.

The 15 successes and failures condition is met.

(c) What is the p-value? (Use 3 decimals.)

(d) What does this p-value mean?

The p-value is the chance of observing 40 or more children with genetic abnormalities in a random sample of 369 children, if the true proportion of children with genetic abnormalities is 10.84%.

The p-value gives the actual percentage of children who have genetic abnormalities.

The p-value is the chance of observing 8% of children with genetic abnormalities.

The p-value is the chance of observing 40 or more children with genetic abnormalities in a random sample of 369 children, if the true proportion of children with genetic abnormalities is 8%.

(e) What is the conclusion of the hypothesis test, for α = 0.05?

Reject H₀. There is sufficient evidence that more than 8% of this nation's children have genetic abnormalities.

Do not reject H₀. There is insufficient evidence that more than 8% of this nation's children have genetic abnormalities.

Reject H₀. There is insufficient evidence that more than 8% of this nation's children have genetic abnormalities.

Do not reject H₀. There is sufficient evidence that more than 8% of this nation's children have genetic abnormalities.

(f) Do this study show that environmental chemicals cause congenital abnormalities?

No, the hypothesis test shows that environmental chemicals do not cause the genetic abnormality.

Yes, the hypothesis test shows that environmental chemicals cause the genetic abnormality.

This study does not address what causes the genetic abnormality.

Expert Solution

Given : n=369 , X=40 , , ,

The sample proportion is , p=X/n=40/369=0.1084

(a) Hypothesis : Vs

(b) Condition :

The children taking part in the study were independent of each other.

The sample was randomly chosen.

The 15 successes and failures condition is met. (np=369*0.08=29.52>15 and nq=369*0.92=339.48>15)

(c) The test statistic is ,

The p-value is ,

p-value=

; From standard normal probability table

(d) The p-value is the chance of observing 40 or more children with genetic abnormalities in a random sample of 369 children, if the true proportion of children with genetic abnormalities is 8%.

(e) Decision : Here , p-value=0.022<0.05

Therefore , reject Ho.

Conclusion : There is sufficient evidence that more than 8% of this nation's children have genetic abnormalities.

(f) Yes, the hypothesis test shows that environmental chemicals cause the genetic abnormality.

Because it was generally believed that genetic abnormalities affected about 8% of a large nation's children.

orchestra answered 1 year ago

In the 1990s, it was generally believed that genetic abnormalities affected about 6% of a large...

In the 1990s, it was generally believed that genetic abnormalities affected about 6% of a large nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities, which could have important implications for health insurance companies. A recent study examined 441 randomly selected children and found that 34 of them showed signs of a genetic abnormality. (1) Which hypotheses should be used to test if...

In the 1990s, it was generally believed that genetic abnormalities affected about 5% of a large...

In the 1990s, it was generally believed that genetic abnormalities affected about 5% of a large nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities, which could have important implications for health insurance companies. A recent study examined 366 randomly selected children and found that 26 of them showed signs of a genetic abnormality. (a) Which hypotheses should be used to test if...

It the 1980s, it was generally believed that congenital abnormalities affected about 7% of a large...

It the 1980s, it was generally believed that congenital abnormalities affected about 7% of a large nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 409 randomly selected children and found that 58 of them showed signs of an abnormality. Is this strong evidence that the risk has increased? (We consider a P-value of around 5% to represent reasonable...

It the 1980s, it was generally believed that congenital abnormalities affected about 7 % of a...

It the 1980s, it was generally believed that congenital abnormalities affected about 7 % of a large nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 356 randomly selected children and found that 48 of them showed signs of an abnormality. Is this strong evidence that the risk has increased? (Consider a P-value of around 0.05 to represent reasonable...

In the 1980’s it was generally believed that congenital abnormalities affected 6% of the nation’s children....

In the 1980’s it was generally believed that congenital abnormalities affected 6% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A 2014 study examined 384 children and found that 30 of them showed signs of an abnormality. Find and interpret a 95% confidence interval for the proportion of all children with congenital abnormalities in 2014. Find the error bound of...

It is generally believed that nearsightedness affects about 15% of children. A school district gives vision...

It is generally believed that nearsightedness affects about 15% of children. A school district gives vision tests to 111 incoming kindergarten children. Use the empirical rule (68%-95%-99.7% Rule) to determine what proportion of nearsighted children we might expect to see in samples of 111 children (I'm not looking for the number of children). Assume conditions are met! No need to draw the model, though if you find it easier to do so you may draw it by hand and attach...

Which type of genetic test can be used to identify genetic and chromosomal abnormalities before pregnancy...

Which type of genetic test can be used to identify genetic and chromosomal abnormalities before pregnancy starts? Amniocentesis Newborn screening Chorionic villus sampling Preimplantation genetic diagnosis In vitro fertilization Sporadic cancer: occurs during one's lifetime occurs in somatic cells affects all cells in the individual A and B only A, B and C Cancer cells are NOT contact inhibited. transplantable. invasive. de-differentiated. immortal. What is the purpose of a pharmacogenomic test? Detection of variants of genes or gene expression patterns...

What are some diseases or genetic abnormalities caused by dominant genes? Why are severe dominant genetic...

What are some diseases or genetic abnormalities caused by dominant genes? Why are severe dominant genetic diseases rarer than recessive ones?

It is believed that nearsightedness affects about 8% of all children. In a random sample of...

It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted. (a) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate? Ho: p = .08 Ha: p > .08 Ho: p = .08 Ha: p ≠ .08 Ho: p = .08 Ha: p < .08 (b) What proportion of children in this sample are nearsighted? 0.1082 (round to four decimal places)...

1. It is believed that nearsightedness affects about 8% of all children. In a random sample...

1. It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted. (a) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate? Ho: p = .08 Ha: p ≠ .08 Ho: p = .08 Ha: p < .08 Ho: p = .08 Ha: p > .08 (b) What proportion of children in this sample are nearsighted? (round to four decimal places)...